Chapter 3 - The Mathematics of Wonderland

Let no one enter who does not know geometry.

(Inscription on Plato's door.)

Geometry And The Limits of Measurement

Mathematics has been used as a primary tool in humanity's efforts to provide maps of reality since the earliest times. Nomads, constantly on the move, needed mathematical tools to calculate direction and distance. Later, as agriculture developed and cities formed, we needed mathematical tools to draw property lines, to record accurately the progress of the seasons on which our crops depended. Traditional geometry provided those tools, tools of measurement. Reality was modeled by points and lines and figures and solids. Geometry provided ways to use measured quantities to calculate the lengths of sides and the sizes of angles which had never been measured.

Geometry as a practical tool undoubtedly predates formal records, though records of property measurements are among our earliest formal records. By 600 B.C. Greek mathematician Thales had already taken geometry out of the stage where it was merely a collection of individual tricks, and had begun geometry as a deductive science. Within the next century, the wonderful theory that goes by Pythagoras' name was formalized (i.e., the square of the hypotenuse of a right triangle equals the sum of the squares of the two legs.) By about 300 B.C. Euclid had systematically collected all known geometric knowledge, and presented it as a deductive science complete with a formal manner of proof. Euclidian geometry was to remain the model for, and primary example of, formal logical systems until the limits of such systems were revealed in the 20th century.

By 150 A.D. the fabled astronomer Ptolemy developed a theory of the movement of the "heavenly bodies", based on the assumption that all such movement was spherical. We now know the orbits of the planets to be elliptical, not circular. In order to make ellipses out of circles, Ptolemy had to construct intricate patterns of spheres within spheres within spheres (or epispheres as they were termed.) This required better methods of calculating angles than geometry could provide. The need for better techniques drove Ptolemy to develop trigonometry. With trigonometry, angles no longer needed to be measured; trigonometry provided a way of reducing the measurement of angles to the measurement of lines.

Measurement reached its peak in the 17th century when mathematician and philosopher Rene Descartes discovered analytic geometry. Analytic geometry provided a way of reducing points to coordinates on a graph and lines to algebraic formulas. Now everything was measurable; everything was reducible to numbers and the relationships between numbers.

However, there was a chink which remained in the structure. Euclidian geometry was a formal method for deriving all geometric theorems from ten axioms and a small number of definitions. Axioms could not be derived from other axioms; they were taken as a given, as intuitively obvious. For example, one axiom said that one and only one straight line can be drawn between two points. That seems intuitively obvious. Unfortunately, one of the axioms, the famous fifth axiom, commonly called "the parallel axiom", was much less intuitively obvious than the other nine: "given a line and a point not on the line, one and only one line can be drawn through the given point parallel to the given line."

This seemed so non-intuitive mathematicians wondered if perhaps it was a theorem, not an axiom. Perhaps it could be derived from the other nine axioms. For over two millennia, mathematicians tried in vain to derive the parallel axiom from the other nine. Alternatively, they tried to substitute some other tenth axiom which could serve the same purpose. But these alternative axioms were equally non-intuitive.

Lobatchevsky's theory [of non-Euclidian geometry] was incomprehensible to his contemporaries, appearing as it did to contradict an axiom whose necessity is based only on a prejudice sanctified by thousands of years.

(The editors of Lobatchevsky's Works.)

Early in the 19th century, Hungarian mathematician Janos Bolyai and Russian mathematician Nikolai Ivanovich Lobatchevsky independently took a new tack. Instead of trying to prove that a single line could be drawn through a point parallel to a given line, they assumed that more than one line can be drawn. A little later, German mathematician Georg Riemann assumed that no line could be drawn through the given point parallel to the line. All three mathematicians were able to derive geometries which were just as logically self-consistent as Euclidian geometry. In other words, they had discovered that geometry is merely a fabrication of the human mind with no necessary correspondence to reality. In fact, when Einstein developed his general theory of relativity, Riemann's geometry turned out to present a more appropriate map of the relativistic universe than Euclidian geometry.

Geometry had developed out of the practical need to measure the world. It had evolved into trigonometry and analytic geometry in turn as the need for still better calculations arose. No one had ever doubted that geometry provided a correct map of physical reality. Then along came non-Euclidian geometry. Suddenly everything seemed in doubt. If geometry didn't necessarily describe the world, were all our measurements useless? After all, measurement was the cornerstone of science. Could there be any mathematics if there was no measurement?

Did we live in a world like Alice encountered when she followed the White Rabbit through a hole in the universe and emerged in Wonderland: a world where people and objects weren't what they appeared to be, where Alice could grow into a giant or shrink to the size of an insect just by eating part of a mushroom, a world where anything could seemingly change into anything else, a world where there were no rules at all (at least no logical rules.)

Living in Wonderland

'The time has come,' the Walrus said,

'To talk of many things:

Of shoes--and ships--and sealing was--

Of cabbages--and kings--

And why the sea is boiling hot--

And whether pigs have wings.'

(Lewis Carroll, "The Walrus and the Carpenter", Through the Looking-Glass)(1)

I personally learned about that Alice in Wonderland world, where logic no longer applied, in my early twenties, through the use of psychedelic drugs. I was lucky that within the first week when I smoked marijuana, I had a mystical experience. The memory has faded, but I believe that while I was thinking about the nature of good and evil, I broke through to another level where I could see that everything fit together perfectly and that neither good nor evil had any distinct meaning. Once back in the mundane world, there wasn't much to hang onto, except an inner conviction that my experience was real and not just a side-effect of the drugs.

Over the next several years, I tried several different psychedelic drugs. While mystical experiences were hardly the norm, I was constantly aware that my perceptions under the influence of the drugs were, in some sense, every bit as "real" as my "normal" perceptions. Though I managed to keep a good job during this period of time, I smoked marijuana daily, occasionally even during work, though more normally outside work hours. Other drugs were usually confined to weekends, though I sometimes broke that rule and came to work when I was still "coming down" off of a drug high.

My experiences with LSD were disappointing, especially as I had expected a great deal from it. For me, LSD was almost entirely a visual phenomenon: It was as if my essential "I" remained unchanged while an incredible "Alice in Wonderland" world went on all around me. The single characteristic I most associate with my LSD trips was the sight of light shimmering down in waves everywhere I turned. Of course, there were many other visual novelties. This largely visual experience seemed inherently trivial to me, since my own ego state remained unaffected. It is likely that my lack of response to this visual experience is an offshoot of inborn preference for kinesthetic experience. When I read narratives about powerful LSD experiences, I assume that the narrator's primary representation system is vision.

Mescaline was a different story, undoubtedly because it was so strongly felt in the body. On mescaline, there was no longer a single "I" concentrated inside my head; instead my consciousness grew diffuse and spread over my entire body. This is very hard to describe to someone who has never taken mescaline. The first time I took mescaline, I let out a figurative sigh of relief when I felt my ego consciousness start to dissolve and diffuse throughout my body. It was if I had been under tension my whole life and was finally able to release that tension for a few hours. As a mild comparison, think of coming home totally exhausted, aching from head to toe, then the sense of release when you sink into a hot bath. I could sit for hours just experiencing the flow of air over different parts of my body, the temperature variation between various parts of my body. After mescaline no one ever needed to prove to me that we are each a whole made up of interconnected parts--I had experienced every part of that whole, both individually and cooperatively. The part I was used to experiencing as my total ego remained, but it was just one of many thousands of parts of my total "I".

Not everyone finds this experience of diffuse ego so comforting. That first time I took mescaline, my roommate waited until he saw how I reacted to the drug before he took it. Reassured by my obvious pleasure, he started about an hour behind me. But as soon as his ego started to dissolve, instead of relaxing into the experience, he panicked and panicked big. I hadn't expected this as he had taken LSD many times and never had any problems, sometimes driving around in his van while high. Even when he had experienced bad LSD trips, which brought out latent paranoia, he had been able to deal with it himself--some part of him remained aware that his paranoia was a construct and had no factual basis. But the mescaline experience was different--he couldn't deal with it at all.

Somewhat reluctantly I pulled most of my consciousness back into my normal ego consciousness (which is itself hard to explain, since I still felt the diffuse consciousness as well, only more attenuated). Then I spent the next several hours calming my friend, reassuring him that things weren't as awful as he thought they were. After that one experience, he never took mescaline again, though the experience didn't put him off further experiments with LSD and other psychedelic drugs.

There was always a flatness to reality after coming down from either an LSD or mescaline trip. Initially I tried to eliminate this by taking more LSD or mescaline when I came down, but I found this didn't work--instead of returning to the high, I just experienced a rather grey in-between stage which had little to recommend it. I had to wait at least a few days in between trips. In any case, since LSD was nothing more than a recreational drug for me, I stopped using it after a few trips. While I initially used mescaline quite often, I began taking it less frequently, not because I wasn't getting anything from the experience, but instead for a very different reason: it had so profound an effect that every time I used it, I needed time to integrate my experience into my normal consciousness. Gradually the intervals between using mescaline stretched out farther and farther. In fact, I can't remember accurately exactly when I stopped using it. When I did quit, it was because I had learned all that mescaline wanted to teach me, and didn't need to take it any more. By this, I don't mean that I could then induce a mescaline state at will, without the need for the drug. It was just that the state was itself only a physical manifestation of something deeper, and that deeper experience was now an integral part of me.

I used the phrase "all that mescaline wanted to teach me" above, instead of "all that I could learn from mescaline", advisedly. I never experienced a true personification of mescaline--"Mescalito", as Carlos Castaneda termed him--but I definitely felt that someone or something more than human was teaching me.

I experienced that same more than human quality in a negative way once when I took "angel dust" (PCP). Together with a number of friends, I had taken PCP for the first time in a party setting several weeks earlier. It was the only non-psychedelic drug I ever took, but at the time none of us were very sure what sort of drug it was. Like mescaline it was a whole body experience, but there the similarity ended. Angel dust felt so good that it was like dying and going to heaven. Trying to find a way to describe it to friends, a rather ludicrous analogy popped into my head from childhood. In a number of "Huckleberry Hound" episodes, Huckleberry Hound himself had a pet dog. When he gave the dog a dog biscuit, the dog would go into fits of ecstasy, rising up into the air and floating gently down horizontal to the ground, rubbing his stomach with pleasure. That's what PCP felt like the first few times I took it.

In retrospect, I realize that I should have mistrusted PCP from the start since it seemed to distort not only sensation, but judgement. The first time we took PCP, I was with a group of friends, and all of us became convinced we were going to live together communally in perfect harmony. We envisioned our little group quickly gaining members until the whole world had joined in harmony. This was so clear and obvious we had no doubt whatsoever that it would happen. When we came down from the drug, our pretty little picture seemed ridiculous--we were all embarrassed and walked around sheepishly, carefully avoiding each other.

I should have stopped using PCP then, but the ecstatic feeling was too tempting to resist--so I continued to use it occasionally. One day, when I was alone in my apartment and took it, I found just how frightening PCP could be. The feeling of physical ecstasy came as it had before, but a voice came as well. It whispered how wonderful it would be to die while in this state. What a wonderful gift to be able to experience such ecstasy, then be able to choose to die at that moment. How lucky I was to have such an opportunity--an opportunity offered to very few people: lucky people, special people, gifted people. This kind of counsel went on and on, for almost four hours. It took every ounce of will-power I had in order to keep from taking the advice.

When I finally came down from the drug and could think dispassionately about what had happened, I tried to decide where that voice had come from. At first, I almost managed to convince myself that it had to be a part of my own personality, and that, therefore, it must reveal suicidal tendencies I hadn't been aware of. But I didn't really believe it--I knew that it was no more a part of me than the mescaline teacher had been. I was dealing with something quite a bit bigger than human proportions. I imagine if I had been traditionally religious, I would have termed it the devil, but I think it would be closer to say that whatever it was, that voice was what leads people to believe in personifications like the devil.

Thus mescaline and PCP introduced me to the non-human forces that can be experienced in altered states of consciousness. People who pooh-pooh magicians calling up angels and demons simply haven't gone deep enough into that nether-world. In an interview in Gnosis Magazine, poet and magical explorer Diane di Prima warned against those who go into the inner world without proper respect:

There's not enough sense of awe, of how real all that stuff is that they're dealing in, and sometimes, because the workings are appropriate, there's some influx of force that is more than they bargained for.[you need to have] just a little more sense that you're really playing with fire when you're playing with fire.(2)

Coffee Cups and Doughnuts

[Topology] would remain true if the figures were copies by an inexpert draftsman who should grossly change all the proportions and replace all the straight lines by lines more or less sinuous.

(Henri Poincare.)

There is actually a branch of mathematics where measurements no longer matter, where doughnuts might turn into coffee cups, much as golf clubs might turn into flamingoes in Alice's Wonderland. Topology asked a very modern question about objects: what is left if you forget about measurement? What if lines can stretch or contract? What if shapes can twist and deform into new shapes? In such a world, does chaos reign, or is there some underlying order that is more central than simple measurement? Topology found that there was order beneath the seeming chaos.

Imagine a sphere made of rubber. Now squash it flat on top and bottom, then on each of the sides, until it becomes a cube. Then grasp a point at the middle of the top side and pull it straight up until the cube deforms into a 4-sided pyramid. If you prefer a triangular pyramid, then push and prod until that's what you have. It would seem that you could transform the sphere into any shape that you like. But appearances can be deceiving in Wonderland. Twist and turn as much as you like, you can never turn the sphere into a doughnut with a hole in the middle, or into a pretzel with two holes.

One of the classic topological mind experiments is to turn a coffee cup into the doughnut you dunk in the coffee. The key is that both have a hole. In case that seems inconsequential, the lack of a hole makes it impossible to transform a cube or a sphere, or any whole object, into a doughnut (nor a doughnut into a cube or a sphere), no matter how you twist and stretch. That's because there is an inherent difference in "structure" between objects with holes and those without holes. Similarly, you can't make a doughnut into a pretzel, or vice versa, because a pretzel has two holes. So some order starts to emerge in Wonderland. Structure is more basic than measurement.

In a dream, a person can appear from nowhere, turn into someone entirely different, then vanish into thin air as easily as they first appeared. Scenes shift without the need for curtains rising or falling; one event can lead into another with no connection discernible to consciousness. But there are connections which are uncovered when dreams are explored. These connections are metaphorical, not logical.

Once upon a time, Chuang Chou (i.e., Chuang Tzu) dreamt that he was a butterfly, fluttering about--to all intents and purposes a butterfly. It did not know that it was Chuang Chou. Suddenly he awake, and there he was, Chuang Chou again. But he did not know whether he was Chuang Chou, dreaming he was a butterfly, or whether he was a butterfly dreaming he was Chuang Chou.

Chuang Tzu.(3)

Which is real: Chuang Chou dreaming he was a butterfly, or a butterfly dreaming that he was Chuang Chou? Is it possible to decide which is which? Topology asks a similar question: how do you decide which is inside and which is outside? It's easy enough with a simple figure like a circle or a square. But what if the figure gets more complex? For example, take a pencil and draw a continuous, non-intersecting, closed figure on a sheet of paper. Don't lift the pencil from the paper until you've finished the figure; that makes it continuous. Don't cross over any lines as you draw it; that makes it non-intersecting. Make sure that you end up where you began; that makes it closed. The following figure is an example of such a continuous, non-intersecting closed figure.

A French mathematician named Camille Jordan proved that such a figure divides the surface into two areas: inside and outside. It's easy enough to see the part that's clearly outside any part of the line you've drawn. How about some arbitrary point surrounded by a number of lines; is it inside or outside?

It's easy to find out; just count the number of lines you have to cross to arrive at an area which is clearly outside the figure. It doesn't matter what direction you take or how complicated a path. If you passed an odd number of lines, your point is inside the figure; if you passed an even number of lines, it's outside. (I've identified two points on figure A, one inside and one outside. Check the rule for yourself using these two points.)

Let's make the problem one level more complex: imagine that the piece of paper stretches miles in each direction. Imagine that, beyond your vision in any direction, someone has drawn an enormous circle which encloses everything, including the figure which you've drawn. The area which you previously thought to be outside, is inside that bigger figure; therefore, the area you thought to be inside is suddenly revealed to be outside.

Of course, it's possible that the big circle might itself be enclosed in a still bigger closed figure; that would reverse inside and outside still again. So within our generalized situation, there is no way to determine which area is inside and which is outside.

However, and this is the significant part, you can still divide points on the surface of the paper into two opposite camps. It's up to you what terms you use for those two areas; inside and outside are fine as long as you remember that you're only talking about a limited frame of reference.

By analogy, the Chinese emperor may not be able to tell whether he is a man dreaming he is a butterfly, or a butterfly dreaming he is a man, but he can distinguish between the two states! Whether one is more "real" than the other is a metaphysical question that won't be resolved with mathematics, but the mathematics of topology does provide a map of how one can differentiate figure and ground, or by extension: conscious and unconscious.

Another basic polarity in topology is left and right-handedness. There is no way to make a left-handed monkey wrench into a right-handed monkey wrench . . . at least not in 3 dimensions! However, you can turn a left-handed glove into a right-handed glove; just turn it inside-out. You can do that because each side of a glove (inside or outside) is a 2-dimensional shape. By turning it inside-out, we are using 3 dimensions to transform a two-dimensional figure.

Well, if we can imagine a 4th spatial dimension, we could take our left-handed monkey-wrench into that 4th dimension, turn it inside out just like we did the glove, and come out with a right-handed monkey-wrench. Nothing simpler . . . but we needed an extra dimension.

I regret that it has been necessary for me in this lecture to administer such a large does of four-dimensional geometry. I do not apologize, because I am really not responsible for the fact that nature in its most fundamental aspect is four-dimensional. Things are what they are . . .

(Alfred North Whitehead, The Concept of Nature)

Topology delights in dimensional paradoxes. For example, let's construct a Möbius strip (named after its discover: 19th century German mathematician August Möbius.) Take a strip of paper, say 1 inch wide and 6 feet long. Bring the two ends together and glue them to make a circle. However, just before you glue them together, give one end a single twist.

That single twist transforms a 2-dimensional figure - a circle - into a 1-dimensional figure - a Möbius strip! Try it out. Let's try to color the outside of the strip red and the inside blue. Take a red felt-tip pin and start coloring the outside. Keep sliding the strip along as you color it. Unless you've seen a Möbius strip before, you should be very surprised when you eventually arrive back at your starting point. Both (?) surfaces of the strip are colored red. There's no inside left to color blue. Note that again an extra dimension was necessary; in this case, a 2-dimensional figure had to be twisted in a 3rd dimension in order to reduce it to a 1-dimensional figure.

Magicians perform a trick called "The Afghan Bands", which is based on the principle of the Möbius Strip. Instead of paper bands, they use strips of cloth, which are easy to tear along their length. One strip is joined into a simple circle. A second is given the twist which transforms it into a Möbius strip before its ends are joined. Both look like simple circles of cloth. When the true circle is torn in half lengthwise, two circles of cloth result. However, when the Möbius strip is torn, you end up with one circle which has a diameter twice the size of the original circle.

Topology provides equivalent figures in any dimension. With 4 dimensions available, a 3-dimensional solid can be converted into a 2-dimensional figure called a Klein bottle. Like a Möbius strip, the outside of a Klein bottle is also the inside. If you filled a Klein bottle with water, the water would flow along the outside of the bottle onto the floor. Or you could just as easily dip the outside into a pail of water and fill up the inside. Unfortunately, we don't yet know how to go into a 4th spatial dimension in order to make a Klein bottle, just as we can't turn left-handed people into right-handed people.

I'd like to discuss one further topological oddity which might best illustrate the difficulties inherent in the development of any topology of the unconscious. This is the famous "4-color problem", which was first presented by Möbius in 1840. Imagine that you're coloring a map and you want to give each adjoining country a different color, in order to distinguish it from its neighbor. How many different colors do you need?

The first of the three circular figures shows the most normal situation, where three neighboring countries come together. But imagine a fourth state situated in the middle of the other three, as in the middle figure, or perhaps a fourth state surrounding the other three, as in the last figure. Clearly you need four colors to distinguish all four countries from one another. But is four enough?


It would certainly seem to be enough. No one has ever been able to produce a map, real or imaginary, which would require more. But, until 1976, no one was able to prove that four colors were sufficient. The way to attack the problem seemed clear enough: list all the different types of ways a map can be grouped and proved the 4-color theorem for each group. The practical difficulty is this approach is that the number of different groups, though finite, is very large (just imagine all the possible combinations of shapes.)

Then, in 1976, Kenneth Appel and Wolfgang Haken, proved the theorem in a most unusual way: they used a computer. First they used traditional mathematical logic to reduce the number of possible situations to a very large number of groups (I believe in the hundreds of thousands.) They then wrote a computer program which painstakingly calculated how many colors were necessary for every group. When the computer determined that no situation needed more than four colors, Appel and Haken announced their proof.

Mathematicians were dubious at first; after all, there had been many previous abortive attempts at a proof. First they examined the logic Appel and Haken used to divide all possible maps into their groups. That was tedious, but open to normal mathematical investigation. No flaws could be found.

At that point, traditional mathematical proof went out the window. There was absolutely no way mathematicians could themselves examine each of the hundreds of thousands of cases which the computer examined. So they were forced to look at the computer program to see if it accurately described each of the groups and forced the computer to examine every group.

No problem could be found with the program code, any more than it could with the formal logic of the proof. And there the situation remains to this day: no one has found a simpler traditional proof and no one has been able to prove the program to be false.

Now consider the original problem which was being examined. Once you have drawn a few examples of possible maps, virtually anyone would be convinced of the obvious truth of the theorem. A map which requires more than four colors seems unimaginable. Yet intuition can't always be trusted and the seemingly unimaginable has turned out to be true far too many times. Without the aid of the computer, any further progress would seem to be stalled. Only a combination of human abilities (used to limit the possibilities) and computer abilities (used to explore the huge number of remaining possibilities) can prove the theorem.

As might be expected, many mathematicians (mostly older mathematicians) still refuse to admit that this symbiotic production of human and computer constitutes mathematical proof at all. Other mathematicians (mostly younger) have realized the power of this new method and are opening up whole new areas of mathematics that can only be explored by a combination of human and computer. This new partnership offers a way to attack problems otherwise unprovable because of human limitations.

With a great deal of trepidation, I would suggest that any attempt to delineate clear relationships between conscious and unconscious might encounter a similar difficulty to that encountered in trying to solve the 4-color problem. The relationships, though open to human intuition and aesthetic sense, are probably beyond the limits of human abilities alone. However, a future combination of human and computer may accomplish what neither could do alone. If so, this would be a truly remarkable instance of the supposedly dehumanizing computer acting in cooperation with human intuition.

ENLIGHTENMENT "BY THE NUMBERS"

In the action of consciousness, we have found three phases: (1) the first nen, which looks outward, working unconsciously; (2) the second nen, which illuminates and recognizes its immediately preceding first nen; and (3) the third nen, which illuminates all its preceding nen, integrating them into the stream of consciousness.

(Katsuki Sekida, Zen Training)(4)

Though I only experimented with psychedelic drugs for about three years, that was long enough to forever convince me that, in large part, we construct our own reality. Almost a decade was to pass before I revisited those alternate states of consciousness I had initially discovered with marijuana, hashish, LSD, psilocybin, mescaline, and angel dust. This second time, I didn't require any outside agency like drugs--I went there on my own through meditation. I started meditating at a very tension-filled point in my life, a time when my philosophy of life was thoroughly materialist and reductionist. In the years since I had taken drugs, I had discarded any "childish" mysticism that might have gotten in the way of a very outer-oriented life. I had forgotten--or at least suppressed--the lessons learned from mescaline. In those days, my little ego definitely thought it was in charge.

Then I started having digestive problems--there is nothing like having to run to the bathroom before you've even finished a meal to get your attention. After denying that anything was going on, I took the usual next step to avoid personal responsibility: I turned to higher authority. I went to a number of doctors who gave me every imaginable physical test. Uncomfortable tests like the upper and lower GI (gastrointestinal) series, where they put phosphorescent fluid in one or the other end, and watch it progress through your intestinal track. I forget the term they used after all these tests to describe my condition, but in summary, it was "we've got no idea, it's probably tension." And that was probably as good a diagnosis as I could get with physical tests.

What I needed was meditation, but I couldn't get there directly. Meditation would have been far too mystical a concept for me in those days. Instead I found a book which presented a technique called "progressive muscle relaxation". Basically the idea was to either sit or lie on your back in a quiet, relaxed setting, then alternately tighten and relax your muscles, moving from the muscles in your feet slowly up the body, until you had visited every possible sight of tension. From the start, I found this to be helpful; however, once I had learned how to use this technique, I knew it was just a baby step toward something else. Next I found a very well-written, scientifically oriented summary of information about meditation(5), and progressive muscle relaxation gave way to a simple meditation of saying a mantra over and over. I tried a number of different mantras at first, then gradually starting using a traditional one almost exclusively ("gate, gate, paragate, para sam gate, bodhi swaha").

Interestingly, while meditation considerably eased my digestive problems, they didn't go away. However, by that time, my interest had shifted away from the problems to the experience of meditation. In fact, though my digestive difficulties gradually grew less and less pronounced, they never went away entirely. When I have periods of tension in my life, the problems pop up again to remind me of the tension. The difference is that the physical problems are no longer center stage. They have just become part of my total environment, a somewhat unpleasant given--like smog in L.A.--but also something that provides a measuring device that is both accurate and impossible to ignore.

Meanwhile, I was meditating regularly--after I had gotten past the baby steps of how to sit, etc., I meditated formally at least twice a day for a minimum of twenty minutes each time. However, I also meditated on an impromptu basis many other times during the day. Whenever I was waiting in a line, I meditated. Whenever I got tired of too much mental exertion, I did a mini-meditation to refresh my mind. After practicing mantra meditation for a relatively short time, I realized that it was also just a step toward something else. I began to explore traditional Buddhist meditation: "sitting" and "breathing". Simple enough--just sit quietly in place and direct your attention to your breath. Once I started this process, I knew I had found the right mode for me, and remained sitting and breathing for the next several years.(6)

"Sitting" and "breathing" presented considerable challenges. Initially my body would protest at having to remain immobile for so long. When my body wasn't protesting, my mind was--no sooner would I direct my attention to my breathing than more interesting thoughts would come to mind. No sooner would I notice that my attention had wavered and try to force it back, than some physical problem would present itself. In my early days of meditating, I was lucky to be able to sit properly and watch my breathing for a minute or two of the twenty minute sessions. I fought with myself, and no one won. In time, the process grew easier--I learned not to struggle against the protests of my body, or the wandering of my mind. When my body ached or my attention wandered, I merely noted that fact, then directed my attention back once more to my breathing. After quite a while, I started to find that all these distractions largely went away and I could just sit and breathe.

It wasn't long after that accomplishment when I found that my body would seem to vanish. This sensation had some similarity to my experiences with mescaline. There I had felt my consciousness diffuse over my whole body; here I felt my consciousness diffuse further until it seemed to vanish. Or perhaps an alternate description is even closer: my consciousness narrowed down until it wasn't there. Though the two descriptions--diffused consciousness or narrowed consciousness--may sound contradictory, in practice they weren't. There was still an awareness of self at some level, but that level seemed separate from me (if that isn't also a contradiction in terms). Zen Buddhism uses the word "samadhi" (enlightenment) for the higher stages of this experience. Let's call my experience a "little samadhi."

Again this is very hard to describe. People experiencing various levels of advancement in meditation have recorded their experiences, but the experience is not readily communicable.(7) One thing that did surprise me was the extent to which my little samadhi was physiological, rather than psychological. Perhaps I shouldn't have been surprised--since all the effort was at achieving a certain physiological state--but I was, and I suspect most meditators are when they finally achieve their goal. Once I had experienced my body disappearing, it was fairly easy to find my way back to that state again.

What I'd like to emphasize is that finding this place required a physical learning process on my part. There was nothing mystical about getting to a mystical state. I had to develop new skills--"psychic muscles"--in order to get there. Once there, I knew what the experience felt like and recognized the warning signs when the body was approaching the correct state. With that knowledge, it became relatively easy to return to that state whenever I liked. At the risk of being crude, it was similar to the control you have over muscles that you use to "urinate". You couldn't possibly explain to someone else how you can choose to either urinate or refrain from urinating when it's not socially desirable. Urinating or not is under the control of your mind, but it's accomplished by a definite physical process. Learning how to enter a state of "samadhi" (to use the Zen phrase, and I'd again stress that I'm discussing a very small samadhi above) is a physical process, not a metaphysical process.

Breathing stands at the junction between those functions which we consciously control and those controlled by our autonomic nervous system. You don't have to think in order to breathe, yet you are able to take conscious control of your breathing if you like: to hold your breath, or to take quick short breaths in order to pump up your energy. In some esoteric traditions, you learn how to take conscious control of normally unconscious processes. In the Zen tradition I was practicing, you bridge these two sides in a different way: you learn how to become conscious of your breath, yet you don't interfere in the process. Later--much later--I was to discover that this was the metaphor I had to use to deal with my entire inner life: become conscious without interfering in the process. This has been much more difficult that it was to achieve my little samadhi. The remainder of this book will be an attempt to record what little I've learned about how to become conscious without interfering in the process.

In 1979, long after my own drug days were over, I had an important dream that spoke to these matters. In the dream, I was in a cavern, participating in an initiation rite. As part of the ritual, a marijuana joint was passed successively from acolyte to another. When it came to me and I tried to pass it on, it kept slipping from my fingers. Somehow I couldn't hold it long enough to pass it on to the next person in line. I became aware that I had to learn how to do it "by the numbers." When I did so, I was finally successful.

I think that dream was teaching me that it isn't enough to experience alternate states of consciousness. We have to develop control over that process--methodical, "by the numbers" control. This is hardly a new revelation. In every esoteric spiritual tradition, there is a stage of ecstatic union with the universe (or God, or one's higher self, or various other terms for the same experience). At this stage, everything is revealed in its own perfection. However, as soon as the acolyte steps out of the experience, the memory begins to fade. The world around looks gray and desolate in comparison. There is a temptation to keep returning to the ecstatic state in preference to the mundane world in which we all live. However, most esoteric traditions rightly regard this as merely an early stage of enlightenment--sort of an adolescence of spirituality. In order to advance further, one has to go back into the world and find a way to incorporate that same consciousness in the normal routine of life.

Zen Buddhists use a series of ten pictures of a man "In Search of his Missing Ox" to describe the stages of enlightenment. The missing ox represents the man's true nature, which all of us lose and have to find again. At the start, the man is sitting at ease beneath a tree. He then notices that the ox is lost, and goes hunting for it. Along the way, he catches a glimpse of the ox, then loses sight of it again. Later he catches it, tames it, and leads it back. At the end, the man is once more sitting beneath a tree, exactly as he was before he began his journey to bring back the ox. Everything is the same, yet somehow everything has changed.(8)

Or perhaps even more succinctly, Zen Buddhist masters say that before enlightenment, we are like animals who eat when we are hungry, sleep when we are tired. After enlightenment, once again we Eat when we are hungry, Sleep when we are tired. But what a difference between eating and Eating, sleeping and Sleeping--the difference between eating and sleeping unconsciously, and Eating and Sleeping with full consciousness.

In my experience, learning to use drugs "by the numbers" required me to:

first realize (at an experiential level) that there is no one single reality--there is probably an infinite number of possible realities to choose from; then

learn the rules of (at least the most important of) these multiple realities; and finally

take responsibility for the choices I made in selecting my own reality.

My learning process has involved moving back and forth between such ancient wisdom (and sometimes ignorance) and modern knowledge (often arrogant foolishness). In both cases, a selection process has been necessary: I have had to distinguish the true core of knowledge from the outer trappings that every tradition acquires over the years. This process has been neither quick nor easy, and continues.

Note: Collage which opened this chapter was created by Simon Miles of Silvan, Australia.

1. Martin Gardner, ed. The Annotated Alice (New York: Clarkson N. Potter, Inc.), p. 235.

2. Diane di Prima, "Gnosis Interview", in Gnosis #2 (San Francisco: Lumen Foundation, 1986), p. 16.

3. Ch'u Chai, The Story of Chinese Philosophy, p. 100.

4. Katsuki Sekida, Zen Training: Methods and Philosophy (New York: Weatherhill), p. 123.

5. Patricia Carrington, Freedom In Meditation (Garden City, New York: Anchor Books, 1978).

6. there are many good books available to explain how one learns to "sit" and to "breathe". I would personally recommend Katsuki Sekida's Zen Training: Methods and Philosophy (New York: John Winterhill, 1975), but many other books have also been wonderful sources for my own development.

7. For those interested, no one has done a better job describing the troubles and travails accompanying meditation than Janwillem van de Wetering in his two books The Empty Mirror (Boston: Houghton Mifflin, 1974) and A Glimpse of Nothingness (London: Routledge & Kegan Paul, 1975).

8. See J. Marvin Spiegelman, "The Oxherding Pictures of Zen Buddhism: A Commentary", in J. Marvin Spiegelman and Mokusen Miyuki, Buddhism and Jungian Psychology (Phoenix, Arizona: Falcon Press, 1985), pp. 43-87 for a psychological analysis of these pictures.

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