In a previous essay (not on this blog), I briefly profiled architect Christopher Alexander and alluded to his magnum opus, the four book Nature of Order. In this essay, I’ll be reviewing the first two books of the set, The Phenomenon of Life (TPoL) and The Process of Creating Life (PoCL). The prominence of the word life highlights the importance of this concept in Alexander’s thinking. For him, life is a quality inherent in all things, not solely a property of plants and animals. This is not a particularly radical belief. It’s a tenet of Buddhism and Taoism, and is beginning to find adherents among some scientists. The thing is, it’s hard to define life in a way that includes creatures like animals and insects, but excludes things like crystals or complex computer programs. Viruses are a good example of the difficulty; are they intricate crystals that self replicate in certain animals, or are they living beings in their own right? Ask a biologist sometime, and see what he says.

In any event, Alexander defines life very broadly, and believes that it exists in the world around us in varying degrees.

So, right away, we find that he is tackling some big questions: What is Life? What is Space? What is the Nature of Order? These are questions that occupy mystics, and there are some who see Alexander that way. I don’t. He is too practical and hardworking, and he is not too concerned with individual spirituality; his focus is on reforming the built environment but, yes, he addresses… spirit.

Spirit is always threatening to disrupt our lives

I wish I could talk about Christopher Alexander without getting into questions about the meaning of life, but it’s no use; the man continually and infuriatingly will point out the 600 pound gorilla in the room that we’re all trying to ignore – humans are spiritual beings, and the world is a spiritual place. We make demands on our buildings that aren’t satisfied by profit and efficiency. That we so successfully avoid this reality so much of the time explains much, Alexander contends, about the often unsatisfactory nature of the world we’ve made for ourselves.

Spirit is always threatening to disrupt our lives; seen in a certain light, the bureaucratization of our society’s large institutions seems designed to prevent such troubling eruptions—see Franz Kafka, Charlie Chaplin, Michael Moore, et al. It is axiomatic that no priest wants a saint in his parish, but then, neither does the mayor, or the factory owner.

Alexander points out that structure, too, can work against human wholeness and spirituality and this seems logical enough. After all, no one leaves nature to get ‘back to the city’ when seeking peace and enlightenment. There are, of course, exceptions. Beautiful gardens or soaring cathedrals can be engines of transcendence. But these are exceptions that prove the rule; generally speaking, the built environment is perceived to repress human wholeness. Why? Why don’t humans create beautiful living structure as readily as do bees, clouds, trees, or termites?

Nature of Order is a work of great detail and great force that attempts to answer this question. That the question of Spirit comes up, implicitly but insistently, is the work’s strength and weakness. The force of Nature of Order is derived from Alexander’s fearless exploration of the structure of the world, and the proper place of humans in that structure. But it also makes his philosophy threatening… a lot of people just want to build a better house, not wrestle with questions about the ontological grain of the universe.

Alexander’s confidence can resemble hubris; and sometimes he seems to rely overmuch on intuition when making his points. To read his books well, one must surrender to them. Not abjectly, and not forever, but a certain suspension of skepticism, while reading, helps enormously when trying to absorb the material.

The Phenomenon of Life
In Book 1, The Phenomenon of Life, Alexander gives his fullest and deepest explanation of his conception of life, and why it is more deeply felt in some places and things than in others.

Early in TPoL, Alexander describes an incident from his teaching career that succinctly captures many of the themes of his work, and the reasons his ideas meet resistance. He asks his students to compare two things: a picture of a 7th century illuminated manuscript (the Durham Gospel fragment) and the wall of the very auditorium in which the lecture was being held. Then he asked a simple question – which of the two had more life?

The question met enormous resistance. Not because it was hard—nearly every student agreed, albeit reluctantly, that the graceful, calm-yet-intricate manuscript held more life than the postmodern, brass-detailed wall. The question itself was what created resistance. Just admitting that one artifact can have more life than another was disturbing. If it is possible to enhance the life of a building, then it is important to do so; but the question of life is not being addressed in today’s architectural curricula—except by Alexander.

Alexander finds this ability in humans consistently, and he also finds that resistance is common. When asked, people agree with amazing uniformity on the relative amount of life imbued in various objects. Although the question seems strange, it has an answer. But this is astonishing, because it tends to destroy the difference between the subjective and the objective. Science stoutly rejects data which cannot be measured. Human opinions, notoriously squishy, cannot be measured by any known instrument… but what if humans, in aggregate, are themselves effective measuring instruments?

There is another, deeper reason for resistance. Lurking beneath Alexander’s simple question is a much thornier question: if humans respond to the life of a place, and if life can be detected and worked with rather simply, how is it that so much of the built world works against life? Suddenly, the work of a developer or a surveyor moves beyond the question of profit, and into the realm of religion. Faced with this, it is much easier to fight against the question, and the person raising it. But this is denial.

Alexander makes his case for pervasive life thoroughly and with great cumulative force. He begins by discussing what he calls centers:

“In using the word center in this way, I am not referring at all to a point center like a center of gravity. I use the word center to identify an organized zone of space – that is to say, a distinct set of points in space, which, because of its organization, because of its internal coherence, and because of its relation to its context, exhibits centeredness, forms a local zone of relative centeredness with respect to the other parts of space. When I use the word center, I am always referring to a physical set, a distinct physical system, which occupies a certain volume in space, and has a special marked coherence.” (TPoL, p. 84)

Redefining a word as basic as ‘center’—or ‘life’—seems willfully inscrutable at first, but the idea is actually quite useful. Consider a pond in a clearing; it is not exactly a whole in itself, because it is part of a larger whole, the clearing, which is in turn part of a forest, and so forth. But the pond is something, and calling it a center does help us to see it as a locus of interest in the midst of a larger whole, a locus that influences that larger whole. And the idea is recursive; the clearing is itself one of many centers in the larger forest and influences that whole, which in turn is one center of a larger regional whole, and so forth.

Like Alexander’s earlier concept of a pattern language the value of the concept lies in its use. Learning to analyze wholes in terms of centers makes it easier to actually see how a whole is formed, and how it can be strengthened or how it is being weakened. It gives those who are trying to analyze space an effective analytical tool.

If it seems presumptuous of Alexander to redefine a word for his own use and to propose an entirely new way of analyzing the world, well, that is a valid criticism but it is also pretty much the point of TPoL. Alexander is proposing a new way of perceiving and analyzing space—he is proposing the basis for a new theory of the world’s geometric underpinnings. Whether he succeeds or not is for each reader to decide.

Living wholes, then, are made up of strong centers, and the life of a whole is increased by strengthening and increasing its centers. As I began to get comfortable with this idea, I indeed found it to be a useful way of looking at the world around me, a way to figure out why I like some places more than others. TPoL is copiously illustrated, and the illustrations do help to convey what Alexander is getting at. But ultimately, an interested reader will have to decide for himself how useful the idea is.

Alexander continues his argument by explaining why some centers have more life than others. And here, I think, he presents an idea that is extremely compelling and immediately useful. It amounts to a general theory of aesthetics, and will likely be adopted rather quickly in the field of visual arts.

Alexander proposes that there are 15 fundamental properties—structural features—that appear consistently in things which have life. Let’s just list them:

1) Levels of Scale
2) Strong Centers
3) Boundaries
4) Alternating Repetition
5) Positive Space
6) Good Shape
7) Local Symmetries
Deep Interlock and Ambiguity
9) Contrast
10) Gradients
11) Roughness
12) Echoes
13) The Void
14) Simplicity and Inner Calm
15) Not-Separateness

About a third of TPoL is devoted to a masterful exposition of this idea. The 15 properties are shown and discussed in manmade artifacts and in natural phenomena. The illustrations and text work together and gather force like Ravel’s Boléro, culminating in an essay titled A New View of Nature. Ultimately we realize that Alexander has done an amazing thing; he has made it possible to talk, really talk, about why we like some things and places better than others. Rather than falling back on vapid words like ‘pretty’ or ‘awesome’ we can speak with precision about the qualities that distinguish Yosemite Valley from, say, a gravel quarry, or why we are more moved by a giant sequoia than by a mall. His beliefs and accompanying language legitimize human feeling, validate our intuitive sense of value, and, without hubris or solipsism, make the world personal.

I have barely skipped a stone over the surface of this remarkable book. In 476 exhaustively illustrated and footnoted pages, Alexander rigorously makes the case for his new view of the world, and takes initial steps toward a mathematical statement of that view. It is an intellectual tour-de-force and fully supported by his real world work as a builder and architect. Such seriousness commands respect; dismissing Alexander casually will not do.

The Process of Creating Life
Defining life is a good start for Alexander, but the major theme of his career has been actually getting more life into modern buildings. And to do this, Alexander found, more than a definition is needed; the what of creation is pointless without the how. That is, a living building cannot be designed, then built. The life of a building comes from decisions made during the construction process. Design and construction turn out to be pretty much the same thing.

Alexander begins to talk about this by returning to one of Nature of Order’s fundamental questions: why is it that natural processes automatically create beauty and a feeling of rightness, and human methods so rarely do? What is the difference?

In a series of fascinating examples ranging from a wave breaking to a glass plate shattering to a fetus developing, Alexander shows convincingly that development processes in nature are a series of structure-preserving transformations. Each recognizable phase of development follows naturally from the preceding phase. Put another way, each phase of development preserves and extends the wholeness of the preceding phase—the wholeness is never destroyed, it unfolds into a new wholeness.

Consider the famous sequence of photos of a splashing milk drop. Though discrete phases of the sequence are startlingly different from each other, the changes from moment to moment are gentle and comprehensible. Alexander argues convincingly that this is a feature of all natural development.

Furthermore, the structure-preserving transformations can be analyzed in terms of the 15 fundamental properties introduced in TPoL. As extended here, the 15 properties become 15 transformations. Change that preserves wholeness is shown to be a product of transformation based on one or more of the 15 properties. Each transformation introduces, preserves, or strengthens one or more of the 15 fundamental properties. Again, one of the most useful things Alexander has done here is to provide good language, which makes good analysis possible.

He goes on to argue, with multiple examples, that humans can build in this structure-preserving fashion, but usually don’t. To do this, he juxtaposes traditional (or pre-modern) building processes with modern examples. He is getting at something deep here; humans love old places. We visit New England, or Europe, to see the old buildings, not the modern ones. We have a sense that the old cathedrals, the old city layouts, are somehow richer. Alexander contends that traditional building methods followed the structure-preserving process he finds in nature. For example, he presents a series of plans that show the development of Amsterdam from 1400 to 1800. It is easy to see how the steady development process took previous development into account. Patterns that were latent in 1400 are realized in 1800, building shapes echo each other, the relationship of the town to the water is consistent throughout. There is no sense of planned development—Amsterdam seems to have grown.

The structure-preserving process occurs in the modern world, but more rarely. Beginning about 1900, many forces—changes in banking, in zoning, in planning, in architecture, etc.—began to produce structure-destroying transformations. The wholeness of an existing structure was no longer considered. A classic example would be the extension of a freeway through an existing neighborhood. The freeway is designed and built without reference to its surroundings, and thereby destroys those surroundings. And similar examples can be cited ad infinitum: a skyscraper designed on one continent and built on another, a planned community laid out with equal precision on the drawing board and on the ground, a giant Wal-Mart box seemingly dropped from the sky onto its scraped pad… in every case, the previously existing whole is disregarded and destroyed.

Alexander uses these examples to define two kinds of structure: generated and fabricated. Generated structure creates life, and fabricated structure, nearly always, creates… the opposite of life.

The discussion of generated structure begins with an analogy that struck me very powerfully. Consider a fairly complex origami construction. It is not built to a plan; that is, blueprints of the finished structure are not provided. Instead, a sequence of steps is provided. A plan of the figure would be quite complex—several pages at least. But a sequence—first do that, then do this—is relatively concise. This idea is then applied to the development of an embryo. DNA does not store a blueprint of the exact appearance of a particular animal, it stores a sequence of development which then takes place affected by attendant circumstances. Interestingly, this is proved by recent experiments in biology—cloned animals do not look exactly alike. Same sequence, different circumstances.

Brutally compressed into a nutshell, Alexander’s program for creating living structure is to generate a construction sequence that first, observes the whole, then, makes a change that preserves and enhances the whole while approaching the desired end state, then… repeats as needed. Or, in his more elegant language:

“A living process is any adaptive process which generates living structure, step by step, through structure-preserving transformations.”

These sequences can also be called patterns, harking back to Alexander’s early book, A Pattern Language. Here, they emerge as part of a comprehensive program for reforming human construction methods. As argued, the case for reform is convincing and ultimately hopeful. After all, the remaining remnants of traditionally built structure are good evidence that humans can build in a living fashion. As a species we have been unconsciously competent, are now unconsciously incompetent, but are beginning to notice deficiencies—to be consciously incompetent. It certainly seems possible that the human capacity for self-observation must eventually lead to conscious competence, and to a beautiful living world.

PoCL is a massive book, totaling 635 pages with appendices and notes. The illustrations are copious and superbly complement arguments put forth. I have, therefore, presented barely a skeletal outline of the book’s full force, but I hope I have adequately suggested that it is forceful.

In some ways, Alexander is the living human I most admire. He has, after all, come by his ideas the old-fashioned way… he’s earned them. He has poured his life into his writing and philosophizing and then he has done something harder. He has, for decades, tested his philosophy, often in difficult conditions in the poorest regions of the planet. He is, simultaneously, an idealistic ivory tower dreamer and a pragmatic contractor; that dirt under his nails is a mix of grit and ink and it’s been there for decades. When a man so rigorously tests his ideas in the real world, over such a span of time, and then adjusts his ideas to accord with the practical knowledge gained… well, he deserves a hearing.

Medicine wheels are great circles of stone, quartered by spokes emerging from a central hub. About 70 are known to exist, mainly in the northern United States and southern Canada. Little today is known about their use by past cultures, though it is assumed that medicine wheels were ceremonial or religious in nature.

We are not the first civilization to be puzzled by medicine wheels. Many of them are thousands of years old, and over the millennia many civilizations have flourished and receded in their territory. And all these cultures made some accommodation with these mysterious stone wheels. Above all, they maintained the wheels; they kept them in repair and extended them, made them larger. Even today they are carefully preserved. So the meaning attached to the wheels has changed over time, but for thousands of years humans have served these patterns in stone.

When I worked as a land surveyor, I served a pattern that stretches over much of the United States. The sectional survey system is the arrangement of grids that divide rural landscapes into square fields and straight roads. Parts of it are nearly 200 years old, and surveyors like myself maintain it by periodically restoring corner monuments. Like any civilization, the American experiment will someday be replaced by another, but the sectional survey system will likely survive—it is ingrained in the land, has reshaped the very contours of that portion of the planet in which it lives.

Patterns do live. They come into being and grow for a while. They evolve, multiply, and sometimes die. They interact with humans and other life forms. Their lives are played out in geologic time, but if we could somehow grasp their movements over thousands of years we would observe all the features of this thing we call life. And from that perspective, humans would seem like cells or helpful bacteria, small pink things rushing about, maintaining the patterns and extending them and eventually discarding and dismantling them.

Patterns are everywhere. Languages are huge patterns, continually maintained and evolved by humans over millennia. Some, like english or mandarin, prosper and grow while others die off.

Religions, corporations, governments; these too can be seen as patterns, ordered systems that persist over time, made up of humans but living far longer than humans. And, of course, even the human body is a sort of pattern; we’re all very comfortable with the idea that our cells switch out every seven years or so, but think what that means. It means that the body is not constant, but some template for the body, some pattern, does endure.

Really, is it too much too say that everything is a pattern, made up of other patterns, nesting and interlocking in exquisite hierarchies of order that endlessly repeat and replicate and die back and rise anew? And that is something to think about; what patterns are we creating and being created by while we live, and when we die, which of those patterns will endure and even, perhaps, live forever?

I happen to be a Registered Land Surveyor, licensed in the State of Wisconsin. I am, therefore a government certified expert in the art of laying out large patterns, such as subdivisions, on the ground. So let’s talk crop circles.

My musings on crop circles usually take the form of an imaginary client who walks into my office and asks me if I could lay out a large pattern in a wheat field. “Sure”, I say, “I have the equipment and personnel to do that.” But then he says, “Well, the work has to be done all in one night. And you have to mash the wheat down neatly, without breaking it off – in fact, you have to bend it a few inches above the ground and weave it into a basket pattern. There will be people looking for you but you can’t be seen and you can’t leave footprints. The pattern I want you to make is quite large, several hundred feet across, and it’s kind of complicated. Oh and, by the way, it’s not my field – and the farmer has threatened to shoot trespassers.”

Oh and, by the way… it’s not my field

So I show my imaginary client to the imaginary door in my mind, but then I get to thinking… jeez, could I lay out a crop circle, given the above conditions? And you know what? Maybe. Maybe I could if I had a big crew and practiced a lot, and if the field was lit and it was dry… but then I think, no way. Not if the farmer wasn’t cooperating. Not without being seen.

But the fact is, at least some formations are hoaxed, and by some very talented people. Working for pay, some hoaxers have made very large formations as advertisements or for TV programs. But… all the formations that have definitely been hoaxed were made in the daytime, on rented fields, with the help of large booms so that the formation could be seen from above.

Here are a few things that haven’t happened: no hoaxer has ever announced a complex pattern in advance, no hoaxer has ever been caught in the act, no hoaxer has ever been interrupted and left a large pattern half-finished, and no hoaxer has ever demonstrated a good technique for creating the often extraordinary weavings formed by the bent crop.

In the end, beliefs about crop circles are a lot like beliefs about Bigfoot, the Illuminati, aliens, and God. One has to consider the swirl of evidence and counter-evidence, and make a decision. And as always, only fools and madmen are ever absolutely certain.

Well, you’ve listened to me this long; it seems only fair to tell you where I stand on the issue of crop circles. I believe that conventional hoaxers don’t account for all crop circles. I believe that at least some crop circles cannot be explained by use of any known human technology. I believe that crop circles are a manifestation of some advanced intelligence. And, most of all, I believe that a crop circle tattoo is a good way to secure a position of oversight in the post-alien-takeover world.

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Cave exploration is not for everyone, in fact it is for very few. Just reading about it can make a claustrophobe cringe. But for those few, those strong, fit, physically narrow and psychologically hardy few, an entrance to an immense world, almost a different planet, is available in Central Kentucky. The massive limestone stratum that underlies that region has been carved by the waters of the Green River Basin, and the mapped stretches of labyrinth in what is now known officially as the Mammoth Cave System total more than 360 miles, making it the world’s longest by a factor of three. It is a wonder of the world as impressive as any mountain, glacier, or ocean but but photographs can only capture slices of it and few humans will ever grasp it as anything like a whole.

Accurate surveying of the cave system began in 1908, when a young German mining engineer named Max Kaemper came to the area, intending to visit for two weeks. He ended up staying several months and produced an accurate map of many miles of cave passage, including several new discoveries. He set a precedent that has endured; exploration, discovery, and surveying are nearly synonymous in this sector of the planet, more closely entwined than in any other human endeavor. Disorientation underground is the default state; it has even been said that a sense of direction underground is something of a handicap, because the circuitous passages so often double back on themselves. When exploring new passages, cavers will sometimes stumble into a known section and reel with vertigo as they reorient themselves. Explorers can push on a bit from known regions, looking backwards often, and find their way back. But only careful surveying and mapping make it possible to have a sense of the cave as a system, locate new passages, explore them, and return safely. Without maps, far fewer miles of cave passage would now be known.

Beginning about the 1950s, it became apparent that careful surveying and mapping were also the key to connecting cave systems, a goal of exploration that is unique to caving and which attained its fullest expression on September 9th, 1972. That’s when a party of six cavers, led by John Wilcox, then Chief Cartographer of the Cave Research Foundation (the body that has organized Flint Ridge exploration for several decades), entered the Austin Entrance of the Flint Ridge Cave System and left through the Elevator Exit of the Mammoth Cave System, thus connecting the two and conquering what had become known as the “Everest of Speleology”. One team member, a small, tough woman named Pat Crowther, compared the experience to giving birth.

At the time, the Flint Ridge System was already the world’s longest known cave system, with 86.5 miles of mapped cave passage. The Mammoth Cave System was not too far behind at 57.9 miles of mapped cave. Between them was a deep valley that seemed to sever the most promising passages. Connecting the two was an awesome event in speleology, much like finding a way to stack Mt. Everest on top of K2 to create the new world’s tallest mountain – some even called it the ‘Holy Grail’.

The actual moment of connection could hardly have been more definite, or more dramatic. A series of remote Flint Ridge ‘leads’ – promising new passages 10 hours or more from cave entrances – had been systematically explored for several months. One expedition had even found scratched initials of early Mammoth Cave explorers, suggesting strongly that a connection was at hand. But the actual route remained frustratingly elusive, and optimistic parties would often return the way they came, crawling and wriggling for hours at a time rather than walking out the easy way. Wilcox’s party faced a particularly heart sinking moment; after nearly a day of work, they knew from survey data that they were within a few hundred feet of the Mammoth Cave System… but they appeared to be blocked by a ‘siphon’, a section of river with no airspace. Wilcox decided to take a closer look, and found that in fact he could duck carefully through the worst section. When he pushed on he saw, up ahead… a straight line?… could it be… a railing?! It was, and Wilcox turned back to shout to his companions, “I see a tourist trail!” – the words became immortal among cavers. Wilcox later wrote, “My memory of the next few moments is indistinct. Victory is a feeling of vastness inside the skull. In this case, it is doubly sweet because it seemed so far way only moments before.”

This awesome moment would not have happened without the careful, cumulative work of hundreds of cavers over several decades. In particular, meticulous surveys were essential. Intuitively, it would seem that surveying would come after the pathfinders pushed new routes and came back to tell the tale. Alternately, it seems that cave exploration might follow the ‘base camp’ model of mountain expeditions, with a few individuals pushing deep into the cave for days at a time, supported by ‘porters’ schlepping in food and other supplies. But neither approach held up to the realities of Flint Ridge caving. Without surveys, pathfinders had no way of knowing where they were in the vastness of the cave system, and no way of telling others how to follow and build on their lead. Of course, some cavers like that aspect of caving – the thrill of having miles of cave forever to oneself – but under the aegis of the Cave Research Foundation, Flint Ridge exploration was remarkably cooperative, with most of the teams involved contributing to the gradually accreting knowledge of the system. Conversely, the base camp system didn’t work, at least in Flint Ridge, because it was terribly inefficient. Resupplying and sleeping underground took enormous amounts of energy. ‘Blitzkriegs’ with occasional cat naps turned out to be the right formula.

The system eventually settled on worked for team players and individuals, and is probably the single factor most responsible for the great successes of Central Kentucky caving. Caving parties of (typically) four would strike out on long expeditions, sometimes lasting 24 hours or more. Support crews on the surface stood ready to assist. The underground teams would go to the furthest limits of explored cave and begin surveying, so that surveying and exploration happened more or less simultaneously. There were variations. On occasion, a party would explore several hundred feet (a very long distance in the twisty, narrow passages) and then survey back to known areas. But this method was frowned on; too often the surveys were left ‘hanging’ – not connected – and were useless. A better system was when two parties surveyed together, leapfrogging each other and moving relatively quickly.

The resulting maps were maintained obsessively; reading histories of Flint Ridge caving suggests that donating rooms – or whole houses – to the maps was a good way to become president of the Cave Research Foundation and perusing ‘map walls’ was an occupation nearly as absorbing to veteran explorers as actual caving. The maps definitely took on a life of their own, and even have an application outside the Mammoth Cave System. Portions of the maps were used as a template for the early (and groundbreaking) computer game “Adventure”, and aficionados have been known to recognize rooms and passages solely from game descriptions.

Equipment used was (and is) sparse compared to modern surveying; it resembled colonial surveying. The use of tripods, total stations and prisms was literally impossible in some passages, due to bulk, and merely impractical in most of the cave. Survey equipment had to be small and light. So Flint Ridge cavers relied on tapes and compasses with built in inclinometers for their surveys, a minimalist set of equipment that has been in use for hundreds of years. In ‘stand up’ passages, the procedure is straightforward: the compass is used to determine direction, inclinometers measure vertical angle, and the tape is used to measure distance. A good survey will also include sketches of the passage cross section, to give a sense of volume. Simple. But doing the same thing in tight tubes or watery channels is difficult and tedious; in some constricted areas, cavers have to back out of a passage after taking a reading so they can move their hands enough to take notes. Keeping the field book dry is a constant consideration. And sometimes progress is painfully slow – in difficult areas, sight lines of just a few feet are common meaning that it takes dozens of readings to get through short passages. To do this kind of work many hours from a cave entrance, with the prospect of a difficult return journey, seems superhuman… and perhaps it is. Certainly there are very few who attempt it. But the work has been done, and done well; the overall mapping error is believed to be within about 0.3%.

The connection of the Flint Ridge and Mammoth Cave Systems was as momentous as any achievement in the history of exploration. It built on several decades of difficult work by hundreds of individuals. It’s curious that cave exploration isn’t as closely followed as, say, mountaineering – perhaps it’s because one can’t see a cave, not in the way a mountain or ocean can be seen. But the physical work involved, and the privation, loneliness and danger, make cave exploration one of the most difficult of sports. The achievements in Central Kentucky, though underground, are one summit of human endeavor.

The above was drawn largely from The Longest Cave by Roger W. Brucker and Richard A. Watson. It is a splendid book, one of the great classics of adventure writing. If the above has piqued your interest even slightly, you will thoroughly enjoy reading this superb tale, told by two veteran cavers. Additional information, and a much appreciated review, was provided by Bill and Sarah Bishop who were elite members of the Cave Research Foundation during the connection era – Sarah is a past president of the Foundation.

A couple of weeks ago, the Diva and I found, and walked, the labyrinth pictured below. It’s at Land’s End, and has a great view of the Golden Gate Bridge. It’s one of at least four in San Francisco—there are two at Grace Cathedral, and one at the California Pacific Medical Center; as it happens, I’ve walked them all. The Land’s End labyrinth is easily the most vulnerable of the four, made simply of rocks and gravel found nearby and raked and set into the labyrinth outlines—in fact, it’s been destroyed by cretins, and remade, at least once. It’s beautifully sited on a promontory, with a spectacular view of the Golden Gate Bridge and the bay. Though it must have taken substantial effort to make, and appears timeless, in fact it was laid out in 2004 by one man, Eduardo Aguilera.

The Land’s End labyrinth depends for its survival on the kindness of strangers, and as the Diva and I negotiated its twisty inevitability we both, without discussion or premeditation, found ourselves tidying and rectifying the pattern by nudging stray rocks back into place. It felt like instinct.

I was reminded of the medicine wheels that appear in (presumably) sacred sites across vast swathes of North America. They are referred to as ‘Indian’ or ‘Native American’ but in fact they are far older than any extant culture and archaeologists tell us that they have existed for several millennia, serving—and being served by—several of the cultures that washed across their range like oceans receding and swelling. Think about that. Medicine wheels—which, like the Land’s End labyrinth are simple patterns of rock laid on the ground—have proven more durable than several civilizations, while also depending on civilizations for their creation, maintenance, and renewal; is it not flabbergasting? Our own civilization protects them carefully, with fences and guards, preserving them for… what?

placing our feet with Jain-like care

Of course, much the same can be said of cities, languages, religions, and other human constructs that outlive humans, and nations, and yet depend on humans for continued existence. It’s as if we are parasitized by patterns of varying complexity who make use of our bodies and minds as a means of life. Think of a medicine wheel filmed from above, its 1,000s of years of existence compressed into a movie of, say, an hour’s duration; it alone would persist while forests shimmered in its margins, while humans, like flickering brown worms, swarmed about and kept it repaired, occasionally adding or deleting pieces of the pattern according to some unguessable logic. I think it would look much like a cell under a microscope, or like a city seen from a satellite. It would be a living, lordly thing, and we its vassals.

The Diva and I walked the labyrinth with something like trepidation, eyes cast down, placing our feet with Jain-like care. I can’t tell you the unknowable vastness of her thoughts, but I know that I was contemplating the labyrinth as a metaphor. Because they are twisty and surprising and yet, in retrospect, inevitable, labyrinths are unavoidable metaphors for relationships, careers, and life itself. And so the walking of a labyrinth should be conducted reverentially, for our passage through it is like our passage through this life. Missteps are likely to find some expression in our circumstances.

I know whereof I speak. For once I walked another labyrinth, with another girl, and though we arrived at its center without mishap she made a fetish of being unrestrained by convention and walked straight out, across the lines, without a backward glance. I felt it like a blow to my heart, and followed her with dread. And in fact that was our last good day together—everything went bad after that, and we both crossed lines that I, at least, came to regret.

These patterns we walk, and live within, and build and maintain and renew; we make them and then they shape us. So much of what we do is set in stone, long before our individual selves exist. So much of what we do is inevitable, but only in retrospect—in the moment of walking, the best we can do is note the lines as best we can and walk with care. And should we choose to flout a line, as sometimes we must, we should do so consciously and face the consequences with open eyes.

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One of the problems with not being a conspiracy theorist is that one has no easy explanations when faced with some of the more glaring oddities of the world around us. It is, for example, passing strange that the dollar bill features an all-seeing eye and pyramid and the fact that it can be explained does not mean that it has been explained, if you follow my drift. Similarly, the non-conspiracy theorist is forced into some fancy mental gymnastics when considering glaringly obvious phenomena, such as the presence of two Skull-and-Bonesmen in the 2004 presidential election (the Bonesmen won either way), the screwy layout of Washington D.C., and the pentagonal shape of the world’s most powerful military headquarters. Mundane explanations exist for all of these, but since they are bizarre facts to begin with, the mind is more comfortable with bizarre explanations involving the Illuminati, aliens, or the occult.

since they are bizarre facts to begin with, the mind is more comfortable with bizarre explanations

My own personal example of this began one morning when I was considering the Public Lands Survey System (PLSS) township layout, the 6×6 boustrephedonic square made up of 36 square mile ‘sections’. ‘Boustrephedonic’, incidentally, is the word for the right-to-left, left-to-right layout of the square – it’s from the Greek, and means ‘as an ox plows’ and in this case describes the descending, switchbacking layout of the square – see the illustration. I’ve always wondered about the township layout; why, for instance, is it boustrephedonic, and why is it 6×6, and not some other number? Idly, I added up the columns and rows, to see if there were any ‘magic square’ properties in the design. The columns all add up to 111 – try it yourself. A little experimentation showed that this is a feature of boustrephedonic squares with even, but not odd, numbered sides, so this is not mysterious. The rows, on the other hand, seemed to yield no pattern of interest… until I took one more step. I ‘reduced’ the numbers numerologically to yield a single digit number. That is, I added together the digits of the multi-digit numbers, and if the result was multi-digit I added again until a one digit number resulted. As seen below, the numerological sum of all the rows is three, and it takes no special flash of insight to see that the numerological sum of 111, the column sum, is also three. Curious.

I should say, here, that I am not much of a numerologist. I don’t work out year numbers, or look for numerological significance in the dates of my life. Still, I did read a book about it once, and took away numerological reduction as a sort of ‘mental fidgeting’. And number mysticism has a history in the West that goes all the way back to Pythagoras and his followers. Many great minds have succumbed, and the results are not always pretty. Isaac Newton, for example, spent at least as much time on numerical Biblical exegesis as he did on scientific work and his writings on those topics strike modern readers as deranged. Many movies, such as Pi and A Beautiful Mind, explore the tendency of the mind to project numerological meaning onto complex phenomena.

Be that as it may and ignoring, for the moment, the possibility that I was succumbing to number mysticism, the undeniable fact remained that the Government Land Office (GLO) township is a numerological magic square. I worked out boustrephedonic squares from 2×2 to 9×9, and only the 6×6 square has this property.

So; now what? Well, not having all that many facts at hand, I immediately began to theorize. Eventually, I came up with rather an elaborate scenario involving Thomas Jefferson, the Illuminati, and aerial photography – it was good for at least 20 minutes of happy hour conversation. But, upon investigation, the hypothesis broke down. Jefferson, for example, preferred a 10×10 square and there is no evidence of Illuminati involvement… but then, there wouldn’t be, would there? So I began to tire of the whole thing; not that I disbelieved my nutty theory, necessarily, but I began to bore even myself.

Kaballah?

It turns out that conventional magic squares are important in Kaballah, and are associated with the planets and astrological magic. The 6×6 square is associated with the sun, and is therefore the most powerful of these. One text of Western Occultism (for which Kaballah is a major source), dating from the 1400s, says of it, “The figure of the Sun is appropriated for kings and princes of this world, and it is square and has a grid of six, and it is the figure of total power.”

early Americans were determined to stamp the ‘figure of the Sun’ across the entire Continent – and nearly succeeded

Now, I only sort of believe in astrological magic, or rather, I’m learning to suspend judgement about the exotic belief systems of others, but it is a fact that humans have apparently always used the progressions of the night sky for mystical purposes, and after 1,000’s of years, astrology very much remains part of our world – something about it is irresistibly seductive to some human minds. And interestingly, amazing feats of engineering have a long association with astronomy and astrology. The Pyramids, of course, and Stonehenge, are just two of the many examples of major ancient accomplishments which are now believed to have been largely motivated by astrological concerns. But considered as a whole, the township system is this planet’s most significant man made feature – it would swallow thousands of Great Walls. It is easily visible from space. Which leads to the rather strange thought that future archaeologists, investigating the wonder that was America, will uncover the whole system of townships and naturally conclude that early Americans were determined to stamp the ‘figure of the Sun’ across the entire Continent – and nearly succeeded.

An Apocalyptic Sum

Here is the key; and anyone who has intelligence may work out the number of the beast. The number represents a man’s name, and the numerical value of its letters is six hundred and sixty-six. –Revelation 13:18, New English Bible

Now What?

Now what is the poor non-conspiracy theorist to do, faced with such a rich source of peculiarity? Probably the best thing to do is to ignore such rabbit holes, but instead I began to wonder about possible motivations. That is, if there were some shadowy group behind all this, what might their motives have been?

Because the GLO square has definitely had a major effect on the United States, quite aside from its impact on surveying. Fly over the United States, or look at aerial photos. You will see a grid, a chessboard; square fields or developed blocks bounded by straight roads. No other sector of the Earth is laid out like this. Fly over any part of Europe, or Asia, or South America, or… anywhere but here, really. You will see roads and fields that follow contours, that give way to hills and mountains, that nestle up to forest edges and creeks. You will see a human landscape that is shaped by the natural world; but in the United States, most of us live in a landscape that is—thanks to ownership lines imposed arbitrarily—imposed upon the natural world, laid over it like graph paper on a map. The township system is part of the structural underpinning of U.S. culture, part of every American’s mental furniture. It may not be, quite, the air we breathe but it is certainly the ground we walk on. It shapes our visible world and it shapes us.

Is it too crazy, too speculative, to say that Americans are a different people as a result of our different environment, that our national culture is partially a product of our national landscape? As a nation, we do tend to ride roughshod, at times, over the natural world. Could our straight roads and square fields be shaping us as much as we shape them?

Now here I speculate wildly, but bear with me. One word for the tendency to impose order on nature is ‘Apollonian’. The sun god, Apollo, has long been associated with classical order, control, discipline and masculinity – as opposed to the Moon Goddess, traditionally associated with wildness, paganism, and femininity. As a nation, the United States is considerably more ‘solar’ than ‘lunar’.

But since the 6×6 square is a solar device, a fascinating (and, yes, nutty and conspiratorial) possibility comes to mind. There is the interesting, unlikely, crazy possibility that some person or group manipulated the choice of GLO township layout in an attempt to cast a Kabbalistic spell over an entire nation… and there is the possibility that it worked.

Of everything I’ve written, the above piece has generated by far the most response. I’m glad. It’s one of those stories that took a couple of years to write, as different puzzle parts fell into place. There were a couple of things I didn’t try to include in the published article (which first appeared in a magazine for land surveyors) or on my radio show. For one, it was really odd how information came to me about this. For example, the occult book mentioned (it is alarmingly titled, Conjuring Spirits) practically jumped out at me from a bookstore shelf and opened in my hands to the Kaballah square that began to tie everything together. Another, weirder, happenstance had to do with my study of a classic ‘master’ conspiracy theory known as the Sirius Mystery, and centering on a book of that title by Robert Temple, and also on an underground bestseller by über conspiracy theorist Robert Anton Wilson titled Cosmic Trigger. The basic idea of the Sirius Mystery is that beings from the Sirius star system visited several ancient civilizations to jumpstart human technology, while also providing the magickal basis for every conspiracy since, from the Knights Templar to the Priory of Sion (don’t ask). Naturally, they are in psychic contact with some humans, and intend to return fairly soon…

Anyway, Wilson’s book mentioned that he and two other writers, Doris Lessing and Phillip K. Dick, all wrote books about aliens from Sirius at more or less the same time, and without having any contact each other. I’d read Dick’s book, and decided to read Lessing’s, Shikasta. It’s a good read, but most notable for me was one of the book’s concluding passages, which described the gridded look of the sectionalized United States and attributed it to the evil ‘Shikasta’ influence! It was an odd moment; two separate conspiracy type thingies that I had been studying and thinking and talking about obsessively for more than a year suddenly and unexpectedly came together with a bang. For a couple of days, the world was a different place for me.

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Think of yourself as a meteorite, zooming through space. Except that from your point of view, you’re not zooming at all; you’re hanging, motionless, with only other meteorites for companions, not even drifting, just endlessly static in a field of stars far denser and more brilliant than atmosphere-bound humans ever experience. Peaceful. Except that every few years, or centuries, or millennia, some damn planet comes crashing through, annihilating you and some hundreds of your brethren.

Meteorite impacts are hard on Earth, to be sure, what with the craters and all… but they’re disastrous for the meteorites.

Peters went further by claiming that the Mercator Projection was inherently racist

The ‘Peters Projection’ was announced by historian Arno Peters in a 1973 speech to the United Nations—the grandiose setting must have seemed a little over the top to serious workers in the rarefied world of cartographic projection. Nevertheless, Peters struck a nerve, and his self-titled projection became very popular indeed—many groups actively lobbied for its use in schools and it was quickly adopted by several U.N agencies and the National Council of Churches for all uses. In 1983 the N.C.C. even published Peters’ book, The New Cartography: A New View of the World. Peters’ map remains in vogue today, being prominently featured, for example, in an episode of television’s The West Wing.

Why all the fuss? What was it about this projection that made it so popular? Well, Peters (who died in 2002) was a master at combining indisputably true points with a few that were disputable. He maintained that the Mercator Projection, then commonly used for wall maps, badly distorted the relative areas of world land masses so that, for instance, Europe looks much bigger than it really is and Greenland appears to be roughly the same size as Africa… when in fact Africa is about 14 times larger. So far, so good, but Peters went further by claiming that the Mercator Projection was inherently racist, and unfit for any use. He based this on the positional and spatial prominence of developed countries as shown on the Mercator Projection. He apparently believed that only ‘his’ map, which accurately showed land mass areas, should be used.

Actual cartographers rolled their eyes at this. To begin with, the Mercator’s problems as a wall map were well known, but to say it had no use at all was crazy talk—it is still indispensable to navigators because straight lines drawn on the Mercator Projection are ‘loxodromes’, lines that show true compass bearing between two locations. In fact, it is axiomatic among cartographers that no projection is suited for all uses—they all have their strengths and weaknesses.

Moreover, Peters was attacking a straw man. Long before 1973 the Mercator’s weaknesses as a wall map were well known and it was gradually being replaced by several projections, notably the 1963 Robinson Projection, the invention of Arthur Robinson, probably the most eminent modern cartographer.

But most damning was Peters’ claim to have invented the ‘Peters’ Projection. Cartographers recognized it as being, in fact, a special instance of the Gall Projection, published in 1885 by Scottish astronomer James Gall. At best, Peters may have independently re-invented it, and the projection is now more properly known as the Gall-Peters Projection.

Buckminster Fuller also gave it a try

For all these reasons, Arno Peters was never going to be popular with cartographers, but aside from that tempest in a teapot, the Gall-Peters Projection still has problems judged strictly on its merits. Though it does allot area accurately, it does so at the expense of shape. Toward the poles, land masses are distorted East-West but near the equator they are distorted North-South; in Robinson’s scathing phase, the resulting maps look like, “… wet, ragged long winter underwear hung out to dry on the Arctic Circle.” Furthermore, other equal-area projections, such as the Albers Conic or the Lambert Azimuthal, have long been available and do a better job of managing unavoidable distortions.

There is no doubt that Arno Peters was a sincere, idealistic man devoted to the cause of fairness and equality. His other major work, the Synchronoptic History of the World, was an attempt to tell the story of all the world’s peoples, giving equal weight to each and avoiding Eurocentrism. He was also keenly aware of the power of ideas and well-versed in the techniques of getting those ideas across—in fact, his 1945 Ph.D. dissertation at the University of Berlin was titled, The Use of Film as a Propaganda Medium. But he wasn’t a cartographer and it may be that his genuine sense of mission and flair for promotion ended up obscuring better approaches to the worthy goal of fairly and accurately representing the world in two dimensions. Nevertheless, he deserves credit for popularizing the issue and for educating the public about the problems of conventional mapping in general and the Mercator Projection in particular.

Arno Peters wasn’t the only 20th century non-cartographer visionary who ended up inventing and popularizing his own map projection—Buckminster Fuller also gave it a try. Fuller (1895-1983) patented his Dymaxion Projection in 1946, based on the simple, brilliant idea of projecting the surface of the globe onto a regular solid. The 1946 version used a cuboctahedron (8 triangular faces, 6 square faces), but by 1954 Fuller was using a slightly modified icosahedron (20 triangular faces) so that the resulting Dymaxion Map could present all the Earth’s land masses without breaking them up. ‘Dymaxion’, incidentally, is a contraction of DYnamic MAXimum tensION and is little more than ‘genius style’ marketing language—Fuller applied the term to cars, houses and even to his preferred sleeping pattern.

As a mathematical feat, the Dymaxion Projection is considerably more sophisticated than the Gall-Peters Projection and consequently has a number of technical advantages. To begin with, distortion of shape and area is minimal and, more importantly, the distortion is evenly distributed. This compares favorably to most projections, which generally distort quite a bit in some parts of the globe but relatively little elsewhere. The Gall-Peters Projection is one of the worst at this since it—somewhat ironically—distorts the shape of developed countries very little but badly deforms the undeveloped countries that Peters was trying to represent more fairly!

The Dymaxion Projection can also be unfolded in different ways for different purposes—that is, the icosahedron can be laid flat with different countries at the center. This avoids much of the almost automatic emphasis that most maps give to Europe and North America, and also avoids the tendency to think of North as ‘up’, thus avoiding a great deal of unconscious cultural bias. In Fuller’s view it was better to think in terms of ‘in’—toward the center of the Earth—and ‘out’—toward the stars.

The most common method of laying out the Dymaxion Map is with the North Pole more or less at the center, and seeing the Earth this way is a revelation. The separate continents appear to be not separate at all! Rather, they look like more like one large island, somewhat fragmented by water but still essentially one mass surrounded by ocean. It’s a compelling view of the world and a startling contrast to any rectangular wall map.

Like Peters, Fuller was a tireless promoter of his many ideas and the Dymaxion Map held a special place because of its role in what he called the ‘World Game’. The game was (and is) played with the aid of a large map that dynamically displays multiple world variables. Fuller’s hope was that the game would evolve into a method for global citizens to directly make responsible decisions about allocation of global resources. To that end, he even produced a basketball court sized version of the Dymaxion Map, dubbed the ‘Big Map’, and presented it to Congress! Though still widely played, the World Game has, alas, so far failed to replace current methods of governance.

Presently, Buckminster Fuller tends to be remembered for his invention of the geodetic dome and little else. One gets the impression that he was simply too prolific to be taken seriously—his ideas and philosophies are so numerous and so far outside the mainstream that it may take the rest of us a generation or two to catch up. But it’s a shame that his unique map is not better known, and almost a crime that the relatively clumsy Gall-Peters Projection seems to have displaced it as an educational tool and wall map. All of Peters’ stated goals—fairness, equality, non-bias—are better achieved by Fuller’s simple, elegant and brilliant creation.

There are several Internet sources for information on the above topics: bfi.org is the address of the Buckminster Fuller Institute and a good start for those interested in Fuller’s life and work, and odt.org sells Peters Projection maps and also has a good biography of Arno Peters.

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Perhaps we are called by urges deeper than we know

The Four Corners Monument, marking the common corner of four southwestern states, can seem perverse and arbitrary, memorializing nothing more than 4 invisible lines coming to a point in desolate country. There is little to do: no rides, no museums, just a few booths selling food and trinkets and the monument itself, a metal disk encased in a massive wheel of imported granite. And yet we do come, by the thousands, driving hundreds of miles out of our way and paying three bucks to stand on the smooth bronze disk, tie our shoes in four states at once, have our picture taken and then… well, nothing; buy some fry bread, perhaps, and then get back in the car and drive to somewhere else. It resembles a pilgrimage, a Southwestern Hajj, a ritual journey to be completed at least once in every American’s life.

Why do we come? Certainly it is beautiful country, empty and serene, punctuated only by massive islands of vertical red rock—and they too are monuments, curiously, of Monument Valley. But it’s like this for ten thousand square miles or more; what is it about this corner of the world – these corners – that so urgently require a visit from so many?

Perhaps it is the contrast between our puny conceptual world and the enduring world of rock and sand. To stand on the monument and spin around slowly is to laugh; the weighty legal lines are nothing to the desert, make no impression at all… and since they lie within another human conception, the Navajo Nation, even their legality is flimsy and attenuated. They barely exist at all…

Or perhaps we are called by urges deeper than we know. The ancient Native American ritual sites now known as medicine wheels were once actively maintained across a broad swathe of North America. They were built according to a simple, immutable formula: a central cairn, radiating spokes, and a circular rim as much as 75 feet across. The stone from which they were made was often packed to the site and the labor involved, stretching across generations, was immense. The Wheel builders are long gone, but here at the the Four Corners Monument we have what amounts to a grand Medicine Wheel, with a central cairn of bronze, a circular rim of stone and cement, and four radiating spokes that stretch for hundreds of miles.

We moderns don’t know, exactly, the use or meaning of the Medicine Wheels, or what role they played in the shifting religious observances of several millennia—that knowledge is lost to time. The same will be true, one day, of the Four Corners; nations, after all, last a few hundred years or less and the desert is forever. But what endures, what will always be as long as humans are, is the making of monuments… perhaps the meaning of a monument is the mere fact of its existence.

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We naked apes have been here before

At the conclusion of a long series of curious circumstances—which is to say, my life—I found myself driving through Houston, on my way to a conference devoted to high-tech land surveying equipment. Such conferences are more exciting than they sound, but they’d almost have to be wouldn’t they? I find them inspiring; the speakers at these events look around at our crumbling world, at the failing infrastructure and dwindling resources, and they see… business opportunity. They believe that technology is equal to the challenge, that new knowledge will keep pace with the horsemen of armageddon, and even pull ahead a bit.

But driving through Houston, I couldn’t help but wonder if the whiz-bang technology that humans are assembling is going to be the saviour of our civilization, or merely its enabler, allowing us to extend our run of resource extraction another decade or two before the inevitable crash.

On the one hand, it’s a dumb question; history, after all, stretches back several thousand years and here we all are, still truckin’. So it doesn’t seem impossible that our species might keep it all together for another millennia or two, at which point it becomes, well, not my problem.

But on the other hand Houston, and cities like it—vast concrete scabs on Pachamama’s skin—seem inconceivable without gigantic inputs of fossil fuels and wishful thinking and they make me quail with dread; they’re the movie sets of apocalypse, and the call for action seems long overdue.

And there is yet another other hand; perhaps it is going to be, has to be, both at once for all our days. Perhaps we will always be going to hell in a hand-basket without ever getting there, quite; always in peril, but never entirely bereft. For we naked apes have been here before. In the 14th century, for example, the Black Plague carried away half our number in Europe and Asia, and in the early decades of the century past about a hundred million of us were felled by Spanish Influenza. We have fought resource wars more or less continually, over wood and water and arable land, over gold and spice and even guano, of all things. And always, when times are bleak and death is all about, our seers and mystics declare that the end of the world is at hand; half in fear, half in glee, they tell us that an angry god will soon be upon us.

The current fashion in world ending cataclysm, at least in my set, is Mayan flavored, and the year 2012 is said to mark the conclusion of history but, of course, the Christians angrily declare that no, their god is the only one who has the right to slaughter us, and the UFO cults and the Kabballists and the extinction biologists all push their preferred catastrophic scenarios. Maybe they’re all right; God, after all, is mysterious above all things and one expects a staggering finale from an impresario like Him. And maybe they’re all wrong; in all our time together on this planet, we’ve always managed to keep ourselves in a panic… maybe we just like the sensation.

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