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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