Into the Morass, Part I

It’s time to begin talking about language, philosophy and Zen. Hence the morass. This is a huge topic which, if approached straightforwardly, has the promise of being transcendental quicksand. I will try to be clear, a hopeless task. But lack of clarity is only to be expected when journeying into a verbal swamp. The real challenge is to avoid a numbing boredom. So I’ll start with a story.

In an Easterly part of Oregon’s Diamond Peak Wilderness lies Fawn Lake, pretty in the summer, but with a much nicer ambiance in the winter. Naturally Fawn Lake is a popular cross country ski destination. Some time ago I was there with friends resting at the shore of the lake on a pristine winter day. The lake was hard frozen, covered with sparkling white snow while in the background behind the sides and back of the lake, with their dark, partially snow-covered firs and hemlocks, rose snow covered mountains, Redtop and Lakeview. These were not huge, impressive mountains, but just large enough to be an esthetic setting for the lake. As we sat there, we heard voices. A party of five or six young folk was approaching the lake via the main trail which comes to the lake fifty or sixty yards from where we were sitting. This trail for the last hundred yards or so runs straight at the lake, surrounded by trees and brush with no view whatever. Then it descends a final slope to the lake shore. We could hear the voices, but could not make out what they were saying, though there was much merriment and banter. One voice was that of a young woman. With my male imagination I visualized her as attractive, witty, but possibly a little empty headed and definitely absorbed with the social situation. As the party descended to the lake there was silence as they concentrated on the final downhill run. Then the female voice came distinctly, “But it’s beautiful.” As she said “beautiful”, her voice faltered and broke. She was clearly in tears.

I’m interested here in the experience she had just before she spoke those words. And interested also in my reaction at the time. I did not break out into tears, but felt a great joy at realizing that a fellow human being had had a wonderful epiphany, had truly seen the scene, and had been overwhelmed by the experience. Where language comes in is that the actual realization experience of both of us here, in the moment this experience happened, was beyond words. Language, the greatest of all human inventions, can talk about this experience but cannot, in thought, re-create the actuality.

I will give further examples of epiphanies and their relation to language. But first I’ll talk a little about the word “epiphany” itself and the related, “mystic” and “enlightenment”. When I use the word “epiphany” I refer to a basic experience of wordless meaning or understanding. The experience may lead later to an expression in words; for example, “But it’s beautiful.” On the other hand, it may be a silent realization of meaning or understanding. The experience may be of different intensities, weak or overwhelming and may or may not be accompanied by emotion. I use the word in a rather abstract way as implying nothing about the world, there is no connotation about “being on a road to Damascus”. For that I would use the phrase “mystic experience”. For me, and I think also in common usage, “mystic” carries often with its intensity an illogical confirmation of a metaphysical, religious, magical, or supernatural reality. Whenever I use “M” word my meaning will include an exposition of the accompanying myth; however, I will not consider the experience as confirming a belief. (More later on this topic.) The word “enlightenment”, the big Buddhist word, is unfortunate in the sense that it may well be meaningless. It can be considered perhaps as some kind of ultimate epiphany. Following the Soto Zen point of view of “gradual” enlightenment, I’ll stick to “epiphany” and let enlightenment take care of itself.

Now to examples of epiphany. Examples obvious to me are the appreciation of music and fine arts. I enjoy lots of music and this everyday enjoyment, I suppose, may be called epiphany lite. A “real” epiphany for me occurs only occasionally mostly listening to classical music in what I would naturally call a great performance. In fact, often I hear a performance that is note and rhythm perfect, as far as I can tell, but I have no deep response. Is it the fault of the performance or of me? Whatever the case, when an intense epiphany does happen with music it is a case where I doubt anyone would claim that the epiphany is not real because it cannot be put into words. Similarly with the fine arts. In the Prado museum, in Madrid I can look at what is perhaps its most famous painting, Las Meninas, with admiration, but without any emotional spark. However, when I walk into the Museum of Modern Art in New York I’m immediately “blown away” and walk from one painting or sculpture to another in a daze of continuous epiphany. Again the actual experience cannot be called up by words or recollection.

With music and fine arts things are simple. With language things are more complicated. One may get into ideas about the “two cultures”, the humanities and sciences, and things get interesting. (With language we’re getting near the quicksand which I’ll try to avoid.) For my first language example, let me introduce the great 20th century physicist, Paul Adrien Maurice Dirac, often referred to as PAM Dirac. Stories about Dirac abound and I will tell one. If you are a non-mathematical reader, you should know that even people with a great aptitude for math and theoretical physics often find themselves at sea. Such happened to a physicist attending a conference during a lecture by Dirac, who, incidentally was a master of clear exposition when it came to technical matters. In this case the confused physicist at the end of the lecture during the question period, raised his hand, stood up, and said something to the effect of “Professor Dirac, I didn’t quite understand the part of your lecture where you talked about ‘blah, blah and blah.’” He then sat down and awaited an answer. There was a very long silence. Finally the moderator said, “Professor Dirac, aren’t you going to answer the gentleman’s question?” Dirac, always very polite and speaking simply to the point, replied, “That was not a question, but a simple statement of fact.” This story is amusing because it shows a genius blind to the conventions of common language. It hints, however, at Dirac’s gift, an ability to see a deep, meaningful structure in the midst of insanely complicated mathematics. With quantum theory, on the one hand, there is linear algebra with its matrices and vectors having an infinite number of components, and on the other, partial differential equations operating on functions, whose arguments are real, but whose expression contain “imaginary” numbers. These two ways of doing quantum mechanics are called “representations” which express different “points of view”. They resemble one another seemingly about as closely as marmalade resembles taco sauce. Dirac, after switching to math and physics from electrical engineering in the early 1920’s, finally made it to Cambridge University. As a student there in 1925 his adviser passed on to him Heisenberg’s first great quantum mechanics paper. (See Paul Dirac in Wikipedia). This paper expounds the matrix-vector representation. Dirac soon saw how to strip away the complex particulars and go to a deeper, simpler, more abstract level, which allowed transformations among the different points of view. The deeper abstract theory in a way is easier to see and understand than all of the more complicated points of view that lead to it. After encountering it, at some point, I came to see it as profoundly aesthetic, simply as a great work of art. Never mind the mathematics. This was my epiphany.

Let me turn now to poetry and its epiphanies. I start by making a muddy, but useful distinction I came up with around my senior year at Stanford. The distinction is between aspects of language. The syntax of language and the semantics. Structure and meaning. Syntax concerns the rules of grammar how sentences are put together. Semantics concerns the meaning carried by language. This distinction is muddy because it does not really hold up. Consider the last epiphany example, the abstract expression of quantum mechanics. The beauty and hence the meaning (semantics) lies in what could be called pure syntax, the structure. However, much of the power of the epiphany came to me from the partly unconscious realization of the underlying “concrete” (sic) mathematics underlying the theory as well as the idea of moving among different points of view, all equally true: marmalade is no better or worse than taco sauce, each is valid with its own joys.

With poetry we have a similar sort of thing going on. When poetry works well a new kind of syntax merges with the words and meaning emerges. Consider a few of the lines from Wallace Stevens’s masterpiece, Notes Toward a Supreme Fiction. Incidentally, before he wrote this poem Stevens thought deeply about the idea of a supreme fiction, an idea we will take up when we again consider myth at some point. Start with the end line of the stanzas I consider.

Life’s nonsense pierces us with strange relation.

A straight prose line that seems to make little sense. However, after reading some of the lines that precede this one, this and the preceding lines become totally mind blasting. The stanzas begin

The poem refreshes life so that we share,
For a moment, the first idea… It satisfies
Belief in an immaculate beginning

And sends us, winged by an unconscious will,
To an immaculate end. …

Stevens goes on… then

We say: at night an Arabian in my room,
With his damned hoobla-hoobla-hoobla-how,
Inscribes a primitive astronomy

Across the unscrawled fores the future casts
And throws his stars around the floor. By day
The wood-dove used to chant his hoobla-hoo

And still the grossest iridescence of ocean
Howls hoo and rises and howls hoo and falls.
Life’s nonsense pierces us with strange relation.

Just reading and copying these lines the epiphany happens to me. However, we cannot program epiphany. You, dear reader may find these lines are simple nonsense without any relation, strange or otherwise. Although as a practice I favor Soto Zen, Rinzai Zen with its Mondos, has an aim similar to that of modern poetry, the aim of inducing a deep epiphany. Getting back to Dirac, once more, he did consider poetry and with his peculiar mind came up with this quote

“The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible.”

Was Dirac unaware he was writing great poetry? Actually I think not. He simply discounted his “mystic” (sic) insights, wrote them down in mathematics and was unaware that they had anything to do with his genius. Such is the false dichotomy between the humanities and the sciences that our culture preaches. More about that in another post.

I’ll bring this post to an end by noting that epiphanies are where you find them; not only in nature, life, athletics, the arts, science, history, engineering, but everywhere, everywhere. The aim of religious practice is to sensitize oneself to their presence, experiencing them in the proper way, seriously, with total openness conscious of their wordless meaning.

Meditation or How I learned to Windsurf

There are millions of writings, of one kind or another, about meditation, of one kind or another. So my challenge here is to say something fresh enough that it will encourage those among you who haven’t tried meditation to do so.

The title of this piece is deliberately misleading. If you think I’m going to show how deep meditation put me in a “zone” so that I quickly mastered windsurfing, you are sorely mistaken. I will find an important connection between sail boarding and meditating, but one of a subtler nature.

My first experience with a sail board was on Dorena Lake near Cottage Grove, Oregon, at Baker Bay County Park.  I was able rent a genuine Windsurfer there in spite of never having sailed such before. This was back in the 1980’s when the very idea of sailing on a board was new and the board sailing craze had barely started. Back then people were not as fussy as now about renting such equipment to total novices. I figured that although I had never sailed a board before, I shouldn’t really have much difficulty. I had surfed respectable southshore summer storm surf at Waikiki and had sailed enough in small boats that I felt confident that I could manage a Windsurfer with only minor difficulties. I had only recently read about this brand new way of sailing and was immediately filled with excitement about the simplicity and freedom of roaming on a board, standing and without paddling. True, there was no rudder for steering on a sail board, but I had read about and understood how one steers without a rudder. If one holds the sail so that most of the sail area is in front of the mast as it pivots on the board, the wind will turn the board down wind. Simply move the sail area back, behind the mast to turn into the wind. To keep moving straight ahead find a judicious balance so that there are equal areas before and behind the mast while making minor adjustments to correct one’s course. What could be simpler? Well, the quote falsely attributed to Yogi Berra is extremely pertinent here. “In theory there is no difference between theory and practice. In practice there is.”

Out on the lake it was breezy, but not too breezy. Conditions were perfect for learning to windsurf, but there were far too many things to keep track of at once. The board was tippy, but not as tippy as my surf board was at Waikiki. The Waikiki board was a sizable board referred to as a “tanker” by the local kids and I could actually stand on it when it wasn’t on a wave. One afternoon when the waves were small and barely surfable, I enjoyed standing on it while the trade winds on my back blew me out to sea where I could catch one of the small waves and ride back in. However, on my Waikiki board there was no mast with flapping sail and I only needed to balance without also trying to think about moving a sail in a wind that would gust, ebb and even change direction. On Dorena I tried to sail up wind by moving the sail back, and, sure enough the board would turn into the wind. And keep turning until I was “in irons”, directly into the wind. At which point I would fall into the water, clamber back on the board, stand up, and carefully lift the clumsy sail out of the water by the up-haul. Then as I pulled the sail into position, the wind would do something funny and I would be back in the water again. After two hours and much effort I was about two hundred yards downwind from where I started, gave up, and swam the board with its sail dragging in the water back to where I started.

As the summer wore on I kept trying to sail and gradually learned how. It was a matter of constant thought, however. Haul the sail up out of the water, while leaning against its weight with up-haul in both hands. Swing the mast and hanging sail forward or back to get the board’s length across the wind. Then keeping balance, reach across and grab the boom using the hand on the side of the body towards the bow. (At first this seems somewhat counterintuitive.) Pull the mast and sail towards the front of the board, then grab the boom with the other hand and trim the sail position as the board starts moving. Try not to lose balance. Then shakily enjoy sailing with one’s butt hanging out to windward until a gust makes one let go of the boom or a sudden drop in the wind ends the support of the sail and one falls backwards into the water.

Winter came and went and with the new summer it was time to try windsurfing again. As I went out on the board I was somewhat anxious. Could I remember all the stuff detailed in the last paragraph? I tried to think as I pulled up the sail. Then miracle. My hand reached across grabbing the boom, forward pull, other hand on boom and I sailed away. Over the winter my muscles and nervous system had remembered and my brain didn’t need to think or remember. This experience was startling because so unexpected. Ordinarily when one learns a skill the body learning is gradual and not nearly as intense and concentrated as when learning to windsurf. Nor is there usually a long interruption, so that the body learning is not dramatically noticeable. Nevertheless in learning any skill, bodily learning though it may not be noticeable, is very real and, I think, very important particularly when it comes to meditation.

Meditation with its emphasis on breathing, lungs and brain involves biological systems that have been under evolutionary pressures for some 300 million years or so, give or take a few million. Not surprisingly we are seldom consciously aware of what goes on as we breathe unless something is seriously wrong with us or we’re climbing at high altitude. With meditation, however, we are not only consciously controlling our breathing but simultaneously hoping that the breathing will help us to empty our mind of thought while keeping it clear and aware. Though the complexity of this task seems less than that of windsurfing, when one gives it some thought, one realizes that there is not simply muscle control involved, but also control of one’s consciousness as well. Ordinarily we are thinking about SOMETHING, or we day dream. In any case our minds are full of thought. Outside of meditation the closest one comes to an empty, aware mind is in an athletic situation – waiting for a serve in tennis or volleyball, or for the “hike” in football or a pitch in baseball. When we are not in athletic anticipation, this empty minded state is highly unnatural and only partially under conscious control. Proper breathing helps.

I first became aware of the idea of deliberate controlled breathing when I discovered in a box of abandoned books The Hindu Yoga Science of Breath. This was during the war, probably in 1944 when Kaiahulu, a vacation house for Castle and Cook employees, was released by the military from its use as an R and R facility. What such a book was doing there I could hardly imagine. I was fifteen. In the book I read of various yoga positions and kinds of breathing, of which the “complete breath” seems to have worked best when many years later I tried to meditate. At the time I had to try the various kinds of breathing and some of the yoga positions, including the improbable full lotus position in which one sits cross legged on the ground with one’s ankles atop opposite thighs. Probably this trial occurred a couple of years after I found the book at a time when I had taken up competitive swimming and was “loose as a goose” so to speak. In a couple of days I did it. Then in a few more days it was easy. And then I forgot it.

After reading about Zen I tried to practice meditation. Although sitting in the full lotus position while breathing in a regular in and out is the supposedly the gold standard, I could no longer come even close to the full lotus so sat simply with my legs crossed and breathed the “complete breath”. To do the complete breath one first notes that by lowering one’s diaphragm one can breathe into the bottom part of one’s lungs behind one’s stomach. Then note that by expanding one’s chest one can fill one’s lungs behind one’s chest. With the complete breath one starts by breathing into the lower lungs behind one’s stomach and then into the upper lungs. This is done in one smooth motion until one’s lungs are full. One stops for an instant and then exhales smoothly and regularly until the lungs are empty. One can imagine while inhaling that a mysterious energy fluid, the Hindu’s call prana, is coming in from the lungs, then up into one’s head all the way to its back leaving a delicious feeling in one’s head as one exhales. As a skeptical physicist I actually believe in prana about as much as I believe in phlogiston or the luminiferous ether, substances which turned out to be fictitious. So I don’t think one should believe in prana either, just experience a feeling as if there were such a thing. Although many people claim that breathing through one’s mouth is the correct way while meditating, I think that breathing through the nose is OK if one’s nose is clear. In my experience one is more likely to get the prana effect doing so. While in a skeptical mood, I’ll also claim that the only reason the full lotus is considered the proper position for meditation is because it enables one to have a straight back and fully fill the lungs. If one sits or stands with good posture, “firm like a mountain”, as one authority puts it, that works just fine in my experience. If fact I just sat straight upright in a chair the last time I did meditation over an extended period. I note however, that when my aunt who was interested in Zen went to Japan, she found that no one would compromise in the slightest their insistence on the full lotus position which for her was impossible because of her age and the stiffness of her joints.

Of course the real catch about meditation is not matters of position and breathing, but settling one’s mind into a blank, empty, alertness, wide awake, eyes open, no thoughts. As a beginner or even a fairly long time practitioner one finds that the clear mind is quickly invaded by thoughts. The proper reaction to this is not to get upset. Clear one’s mind if possible, and keep on going. In the beginning it helps to count one’s breaths – one, two, three, up to ten. Then start over. One can count breaths in and out, just in, or just out. I can’t see that it much matters though at first the in and out seems to work best. Getting back to the example of my first windsurfing experience, the lesson is not to keep going too long when things aren’t working. Then I kept going for two hours because I was sort of having fun. It is clear that another two hours would have been totally exhausting and worthless. With meditation, ten minutes at first is definitely enough. In fact if time is short, ten minutes is always enough to get the practice that leads in the long run to the automatic muscle, nerve, and mind learning.

For those of us living in modern times, with job, family, and countless activities, there is a real question about finding the time to meditate. My own experience is that I would go for years at a time without practicing meditation and then come back to it for several months. More recently the automatic learning entailed by this on and off practice over the years has kicked in and I’ve been able to settle in pretty well to clearing my mind while simply walking around during odd moments when there are no immediate demands on my attention. This practice brings to mind a Russian Orthodox practice called “the prayer of the heart”. Monks who engaged in this practice would constantly pray all day long as they went about their business at the monastery or their begging in the outside community. I’m not at all recommending anything as draconian as the prayer of the heart. However, simply hearing about this practice suggests that an emphasis of setting aside a time apart from the world of daily life in which one practices meditation is unduly limiting. One does the daily meditation so that the complete breath becomes ingrained. Then when one has a spare moment or if one feels unduly stressed start the breathing and clear the mind. Meditation then is not a thing apart but a continuing practice to be engaged in at any time one finds or needs a moment for relaxation in the middle of life.

A final question: why bother with meditation? What good is it? Is the trouble one goes to worth the result? Those who practice meditation note that it does tend to relieve stress and make one’s life go easier. That is certainly my experience. Besides being a stress reliever, meditation does seem to intensify the experience when one has a realization or a moment of insight. In addition, if one thinks that possibly, there is such a thing as a deep spiritual understanding, meditation is a practice that likely helps bring that understanding about.

A Warning

I am very unhappy about the last post: “A Zen Practice.” I feel that it over-promises and is dishonest. It being in a WordPress blog I could delete it, but I will not do that. Let it be a warning about how easy it is to be deluded when on a spiritual journey. Such a journey is difficult, must be pursued with concentration and with absolute honesty. I am nowhere near where I need to be, to give advice to anyone about their own journey. If you become a reader of this blog, then I need your insights at least as much as you might need mine. Please comment when you think I’ve overdone it or if you have an insight to share.

All this being said I still think that there needs to be a Western path towards a deep understanding. Calling it Zen is probably over-promising. I will certainly continue these posts because I do have some things to say and it has been helpful to me to try write with intensity and honesty. If you become a reader, I hope that you gain some insights and perhaps commit to a lifetime journey of your own.

I’m away on a trip for a couple of weeks so there will probably be an absence of posts for a while and I may be slow in reading your comments.

A Zen Path

So is Zen real? My recent feeling is to upgrade the answer from “maybe” to “quite possibly”, after 57 years of often lukewarm practice. I feel my life has been enhanced because my practice has deepened it without necessarily getting me anywhere spiritually. It is better NOT to believe in a practice, keeping a strong skepticism about any possible “enlightenment”. This skepticism enhances and concentrates one’s efforts of understanding life and getting clear about things, one aspect of the practice. Commitment consists of never giving up. As it turns out this practice is a specifically Western approach which I think is appropriate to those leading busy lives in the Western part of the world. It is closest to the Soto School of Japanese Zen which is the school of “gradual enlightenment”. The other main Japanese school, the Rinzai School uses Koans and strenuous efforts in an attempt to induce “sudden” enlightenment. Possibly there could be a Western practice based on the Rinzai School. I think it is partly a matter of personality. If one has a type “A” personality, pursuing goals passionately and rigorously, the Rinzai model MIGHT be appropriate. However, the Rinzai approach probably requires giving up all other aspects of one’s life, such as making a living. One probably would need to join a religious community of like-minded people, which is OK if one is inclined that way. The approach I’m advocating here does not require giving up one’s chosen life, will probably enhance it, and quite possibly lead to a deep spiritual understanding.

In what I’ve said above there is (at least) one possible point of confusion: I may have made it sound like the Japanese Soto approach is not very serious. If you’re left with this impression, it can be dispelled by reading Hard Core Zen by Brad Warner, an American, compelled by religious passion, who went to Japan and learned enough Japanese to work in Japanese sci-fi monster movies (which incidentally are great fun). Warner practiced for years under a Soto Zen master eventually becoming sufficiently aware to be certified a master in his own right. His book is absolutely first rate if one is not put off by his irritatingly colloquial English which is probably part of his shtick. So Soto Zen practice is by no means laid back. However, the Western practice I will be explicating in this blog is INDEED laid back and can easily be charged with a lack of seriousness. The only way to dispel this charge is to ask, does it work? The only proof of the pudding is in the eating. I’m talking here about my own practice, stumbled into inadvertently and almost by accident. The only credit I can claim is a stubborn (lazy) refusal to heed all the warnings about why it couldn’t possibly work. Is it working for me? There are slight hints that it might be. I FEEL that it is. In the face of a personality of great diffidence I recently now feel an outrageous certainty about some things and am willing to be dogmatic. Also, I actually feel an obligation that I must share some insights, a feeling in line with the Mahayana Buddhist idea of the Bodhisattva. Since I’m definitely not on the brink of “ultimate Samadhi”, I can only be an apprentice Bodhisattva, pointing out stumbling blocks and insights I’ve encountered in this kind of practice and using this blog as a Zen art in an attempt to improve my writing skills.

Whimsical Math

These last few days I started to write some more about Zen, but the ideas were ill-conceived and turned to mush. Maybe someday they can be resurrected though I doubt it. To clear my brain I started to write something just for fun. Perhaps it is worth posting.

Whimsical Math

In the series 1,2,3,… what is the ultimate number? Not the largest number, there being no such thing, but the ultimate number. Answer: The last yianh. As 10 or 11 year olds, my brother and I, playing in our upstairs bedroom, speculated about numbers that were so large that it would be pointless to consider anything larger among the infinity of further numbers. There was an entire series of these, starting with the first yianh, a number so large that a googolplex would fade into an insignificant blob near zero. Of course we had never heard of a googol or a googolplex nor did we know anything about exponential notation, but such specifics are pointless when imagining REALLY large numbers. After a huge series of further numbers one would come to the second yianh. And so on. Finally, after many, many more yianh‘s we would reach the last yianh, a super fabulous number that ended our imaginings. I think now that we had some inchoate idea that the entire tail of the infinite integers would somehow be condensed into this ultimate number. Perhaps this is how mathematics gets developed. One plays around and then some idea like making an infinite series finite by coalescing numbers comes up. Then one sees this as a problem. Can the idea be made logical and coherent? If one succeeds, one has created some new math. If the effort fails, maybe the idea can be deployed somewhere else.

In the nineteenth century there lived a very great mathematician named Bernhard Riemann. Actually there were many very great mathematicians in the nineteenth century, but Riemann was one of the immortals, like Beethoven in music or Shakespeare in drama. (Well maybe not quite as uniquely great as Shakespeare.) Anyway Riemann studied a function, now called the Riemann Zeta function. A function is like a meat grinder. With a meat grinder, one feeds in meat and hamburger comes out. With a function one feeds a number in and another number comes out. The number coming out depends on the one fed in so that one always gets the same second number from the same first. Of course, when talking about the Zeta function there is a little complication that is likely to scare you away if you are a math phobic reader. But be reassured. I will explain this complication with the utmost lucidity and make it completely clear or at least translucent by telling a story about numbers.

Since Greek times there have been many developments about what numbers are. Numbers started as the 1,2,3’s. Then someone discovered a big shortcut, called multiplication, when the same number was added up many times. Immediately, problems arose where one needed to go backwards, so division and with it fractions came into being. The integers and fractions together were called rationals. But horror upon horror, the Greeks found that there were crazy numbers, like the square root of 2, that couldn’t be expressed as fractions. These were called irrationals, disturbing because the Greeks were wedded to being rational. Then when considering such things as debts, people realized that negative numbers were useful, and, more important, could be introduced in such a way that no logical contradictions arose. New math had been created. Later the idea arose that the gaps that still existed among the rational and irrational numbers could be filled to make a continuous stream of numbers with again no contradictions. But here trouble arose. One theme of this blog will be the difficulties we get into by misunderstanding language. The new numbers were called “real” numbers although they were the product of human imagination and could easily have been called “numbers of the imagination” or imaginary numbers for short. Of course, when the numbers we now call imaginary were introduced, this introduction caused all sorts of trouble, not only at the time, but subsequently to generations of math students. I certainly was very dubious about imaginary numbers. If they weren’t real, how could they even exist? Well how can any number exist? It exists because it can be used to calculate things without contradictions arising. So, it turns out we can have what are called complex numbers, consisting of a pair of real numbers, though the second of the pair is called imaginary. Consider imaginary as simply a label used to designate the second of the pair. (It is true, however, that squaring this second number results in a negative “real” number, but that’s really no big deal.) These complex numbers can be used without logical contradictions; but raise the question: What about a triple of numbers? Can a triple be made to act like other numbers? The answer is no. The number pairs are as far as numbers can go. (There are more complicated sets of numbers called vectors, but they work differently from numbers.)

Of course, the reason I’ve gone through this song and dance about numbers is that the numbers fed into the Zeta function are complex numbers, as are the numbers coming out. The Zeta function is called a function of a complex variable and such are studied in graduate level courses in math. (When I took the course at Stanford, I flunked, but later picked up some of the subject on my own.) Since complex numbers are pairs of numbers they can be plotted on a 2 dimensional sheet. We plot the first number on a horizontal x axis and the second, so-called imaginary, number on the vertical y axis. An important situation arises when we feed the first number into the Riemann meat grinder and get 0 out of the function. Such numbers are called “zeros of the Zeta function” although they themselves are not in fact zero, but produce zero when fed into the function. They should have been called zero producers, but that is too long-winded for mathematicians. Meat goes in the grinder, but nothing comes out. So call the meat a zero. Anyway, the Zeta function has many zeros some of whose location turns out to be connected to the distribution of prime numbers. Mathematicians call the others “trivial zeros” and study the ones that matter. Riemann calculated a few of the non-trivial ones (turning the crank of the Zeta function is not easy) and found that they lay on a line with the real part = ½ and the imaginary part on a vertical line rising up from ½ on the horizontal axis. Riemann speculated that all of the important zeros would lie on that vertical line with real part ½. He couldn’t prove it. Nor has anyone proved it in the 156 years or so since, though not for want of trying. (Whether true or false the hypothesis has Yuuge consequences.) Zeros in the billions have been shown to lie on that imaginary line, but billions aren’t equal infinity and a proof would show that all of the infinite number of zeros lay there.

I have a whimsical notion that if Riemann’s hypothesis is incorrect, somewhere up in the far reaches of the imaginary line there is a zero whose real part is not ½. I’ll call this zero the first yianh; other violators the second, third, etc. yianh. One wonders if there is a last yianh or does the sequence of violations never end? Note: I strongly suspect that Riemann’s hypothesis is true, in which case my last remark is even more whimsical.

Prime Obsession: Bernard Riemann and the Greatest Unsolved Problem in Mathematics by John Derbyshire is a fascinating book. A history of the times and a biography of Riemann alternate with chapters that go into the math seldom going beyond high school level. Or go to Wikipedia.

A final note: There are hints that the distribution of the primes for large numbers (primes up there with the yianh’s) has a connection with certain physical properties of the universe. It is difficult to keep “pure” mathematics pure.

 

Spiritual Quest, 1958-1959

It is fall, 1957. I am newly married to Barbara, my first wife. We are in Auburn, Alabama where I am a Temporary Instructor in the Physics Department at the Alabama Polytechnic Institute, later to become Auburn University. We have ended up in Auburn because Barbara was acquainted with Dr. Howard Carr, head of the Physics Department and knew that the department badly needed people to teach elementary physics to engineering students and liberal arts majors. Letters written from Innsbruck plus a positive reference from my graduate adviser at Stanford (Georg Polya, a well-known mathematician) sealed the deal. Of course, I had pretty much forgotten the little physics I had ever known so I would need to learn the subject from the text I was teaching and try to stay a week or so ahead of my students. Since I was planning to become a physicist anyway, this was a fun challenge and I didn’t do too badly in meeting it. Certainly, I could appreciate and relate to the difficulties my students were having with the subject. Meanwhile, Barbara had decided to switch her major from mathematics to English literature so was taking graduate courses in the English Department.

That fall we were totally absorbed in life. I was passionately in love with Barbara and working hard on learning elementary physics and doing well with my teaching. As a faculty member I had easy access to football tickets and enjoyed going to games. The Auburn team that year was winning all their games, a new experience for me after watching games in high school and at Stanford. In high school I watched Punahou lose 64 – 0 to Kamehameha in their first game and lose every subsequent game thereafter. Stanford had a similarly bad season my freshman year. In retrospect I think that the Auburn team was the best college team I’ve ever seen. They had an overwhelming defense often holding opponents to negative yardage on the ground. Their games were not exciting because they did not seem to be very fired up. They would get a lead of a few points, shut down their opponents, and play out the rest of the game in a boring manner. There was only the suspense of wondering if the opposition would score on a fluke play. When it came time to play the last game of the season against arch-rival Alabama, the press was wondering if there would be an upset because Auburn’s wins had been less than dramatic while Alabama hadn’t done all that badly. The game started in a usual manner. Auburn won the toss and, as they always did in such circumstances, elected to kick. As the kickoff sailed down the field I suddenly realized I was looking at a different, fired up, team. The Alabama receiver took the ball in the end zone and started up the field, making little progress as flying tackles narrowly missed their target. The runner was shortly overwhelmed at about the 15 yard line. In the next few plays Alabama lost yardage and finally fumbled after a hard hit in their end zone. Auburn 7, Alabama 0. Subsequently Auburn finally displayed their offense. They did have an all-American end, Jimmy Phillips, who played sensationally and their ground game became effective. Final score 40 – 0. What impressed me about that Auburn team was the philosophy of doing the minimum necessary to win, in a relaxed manner, never playing to potential unless necessary or in a game with Alabama. This attitude, with its suggestion of power held in reserve, smacked of the Zen I would later encounter.

Also in that Fall Quarter I was becoming acquainted with Barbara’s family and numerous relatives, taking in the friendly Southern atmosphere, which overlay a terrible racism, seldom explicitly on display to me. However, I knew it was there. The first morning in Auburn I was awake at dawn, still not adjusted to the time change, so got up in the early light and headed to town up the main street. A black man came down the side walk in front of me, began to hesitate when about thirty feet away, then stepped off the sidewalk three or four feet into the street and cowered, half turned away from me with head bowed, as I walked by. I was totally appalled, having grown up in Hawaii where there are too many races and racial mixtures for serious prejudice though people other than haoles (whites) had been quite subjugated in the days before I grew up. By the time I was in high school, however, one could be taunted for being a haole and perhaps beaten up, so what prejudice there was operated in all directions. In Alabama, because I am a realist and definitely a coward as well, I never openly challenged the mores of that time, but tried to treat black people with respect.

A late poem of Wallace Stevens has the title “A Child Asleep in its Own Life”, suggesting the image of a child totally engaged and walking around with concentrated purpose, unaware of what was going on in its surroundings. It seems to me that I and probably Barbara were in a similar state of being that fall. We were fully engaged with our lives and with each other but I had certainly dropped all thoughts of a spiritual journey, of religion, or of anything else beyond our immediate circumstances. Winter Quarter came and things began to change. That quarter I was able to sit in on a class in quantum mechanics taught by Ernest Ikenberry. Professor Ikenberry was in the process of writing a text, loosely based on the quantum mechanics text by David Bohm. At the start of each class he would hand out three or four pages of mimeographed notes and then lecture, explicating the notes. Quantum mechanics for me was a revelation. I loved the mathematics and slowly came to realize that quantum physics totally demolished the deterministic world view of classical physics, a view that I had heartily disliked. I was delighted that physics had opened up in a way that could sit easily beside all the other worlds of human experience. Physics was going to be very exciting.

Another happening that made a huge impression on me was my first encounter with Zen. I can’t remember exactly when this was. Probably it occurred sometime during the Winter Quarter in 1958, or perhaps as late as early Spring Quarter the same year. In any case it came about because that year we were subscribing to Harper’s Magazine. My favorite writer appearing in the magazine at the time was Gilbert Highet whose essays were always interesting and beautifully written. So, it was with interest that I read Highet’s review of Zen in the Art of Archery by Eugen Herrigal, which had been translated from German to English a few years before. Besides talking about the book Highet also had some additional thoughts about Zen Buddhism, which, at the time, was practically unknown in the US and completely unknown to me. Intrigued by Highet’s piece I went to the Auburn library and found not only Herrigal’s book but one or two others by D.T. Suzuki who in the late 1920’s had thought to introduce Zen to the West. Suzuki’s Essays in Zen Buddhism particularly impressed me. Here was a religion with no doctrines or beliefs. One was to discover one’s own insights through meditative practice, aided perhaps, by concentrating on crazy riddles, called Koans or Mondos.

Three things about Zen were apparent to me. First, it was a serious religion. By that I mean a religion that becomes the center of one’s life. Second, because Zen makes no concrete specific claims about the world, it could be the deep, wordless philosophical center encompassing all other more concrete subjects without conflicting with any of them. Finally, if pursued successfully, it had the potential to bring spiritual peace to one’s life in the face of death.

At the time I was by no means converted to the religion. Life was far too busy and I simply didn’t know enough about it. I loved the riddle characteristic of the Koans. They seemed like the problems in physics that I enjoyed struggling with. However, a Koan did not have a rational, mathematical answer as in physics, but a deep non-verbal answer enveloped with understanding – rather like a joke whose point one gets instantly or not at all. (Of course I “got” none of the Koans at the time.) It was clear to me, however, that I would have an enjoyable time ahead learning more about Zen and about the Buddhism it grew out of before I would understand enough for a possible commitment.

As the academic year at Auburn drew to an end there was much on my mind. I had been accepted at the University of Virginia as a graduate student in physics and I was off for a summer trip to the Tetons with Barbara and her young sister Mary, driving an old Ford and camping along the way.

Fall 1958 found us living in a dank basement apartment in downtown Charlottesville, parking the old Ford on hilly streets for more assured starting in the morning, and attending our classes at the University. My most exciting class in classical electricity and magnetism was taught by John Plaskett, English and only a few years older than myself. Starting from Maxwell’s equations he would develop the story of how they came to be and their consequences in a lucid manner. In the afternoon I would spend three to four hours going over my notes, being sure that I understood every nuance of the derivations. In class I always sat in the front row because Plaskett had the charming habit when coming to a key conclusion at the end of a long, mathematical argument of announcing the dénouement in a voice that sank to barely above a whisper. How embarrassingly immodest it would be to be blatant about a beautiful result. I imagined Plaskett as a Zen master who was bringing enlightenment through electromagnetism. If the mastery of archery could bring Herrigal to the brink of transcendent understanding, why wouldn’t theoretical physics serve just as well? Of course I suspect that Plaskett hadn’t the slightest idea he was practicing a Zen art, but I, in my naivety was stumbling upon the idea that depths can lurk anywhere, even in the beauties of a science devoted to understanding the most mundane materialistic reality.

Of course, in my spare time I checked out the University of Virginia library to see what it contained in books about Zen. There was more than at the Auburn library but not so much that I couldn’t read it all during the year. Besides studying physics and reading about Zen I was exposed vicariously to English studies. My fellow physics students remained acquaintances whereas Barbara’s fellow English students became our friends. People studying literature tend to be more articulate and socially interesting than scientists and engineers so we ended up running with the English crowd. Barbara’s most exciting studies were in classes taught by Fredson Bowers, an authority on the textual criticism of Shakespeare. She also had a class in which every poem written by Yeats was read and discussed. In earlier years I had discovered how moving poetry could be so I thoroughly enjoyed the discussions among our friends though my contributions were minimal.

Classes continued during the winter and through the spring and came to an end in June at the beginning of a miserably hot humid summer. That summer we would spend in Charlottesville where I had a job studying and hopefully contributing to centrifuge science. Luckily there was swimming pool, surrounded by a shady lawn where we could hang out and be comfortable in the hot weather. And one afternoon while sitting in the shade with Barbara, cooling off after a swim, I became conscious that I was committing to Zen. Such a decision is not made consciously or rationally. I was very aware that I had little or no understanding and that the whole thing was a big mystery. However, it felt good that I intended to spend the rest of my life attempting to understand what it was all about.

Dream and Myth

Sometime ago I had an unusually vivid dream. I was swimming underwater, perhaps ten or fifteen feet below the surface. I was swimming along with little effort, not holding my breath. Looking to one side I saw that I was swimming alongside a huge shark. I had a moment of panic being so close to such a fearsome beast. The shark’s side was 5 feet from top to bottom, it was about 30 feet long, but it wasn’t a harmless whale shark. Then I looked at the shark’s large eye which was staring at me and noticed that the shark’s gaze was intelligent and somehow caring. Immediately, in the dream I felt not only comfortable but deeply peaceful. When I woke up, I remembered the dream clearly.

Among Hawaiians there is a tradition of having a personal totem animal called one’s ʻaumākua.

The wehewehe dictionary’s definition:
nvt. Family or personal gods, deified ancestors who might assume the shape of sharks (all islands except Kauaʻi), owls (as at Mānoa, O’ahu and Kaʻū and Puna, Hawaiʻi), hawks (Hawaiʻi), ʻelepaio, ʻiwi, mudhens, octopuses, eels, mice, rats, dogs, caterpillars, rocks, cowries, clouds, or plants. A symbiotic relationship existed; mortals did not harm or eat ʻaumākua (they fed sharks), and ʻaumākua warned and reprimanded mortals in dreams, visions, and calls. (Beckwith, 1970, pp. 124–43, 559; Nānā 38.) Fig.., a trustworthy person. (Probably lit.., ʻau 4, group, + makua, parent.) See pulapula 2. hō.ʻau.makua To acquire or contact ʻaumākua.

Growing up in Honolulu one heard much of Hawaiian traditions. At my elementary school we heard Hawaiian stories of how Maui raised the islands out of the sea and, on occasion, learned a Hawaiian chant celebrating the god Lono. So it was clear to me that I had a giant shark god as my `aumakua. This was a source of satisfaction; however, if you ask how seriously I took this as protection if I swam in shark infested waters, the answer is “not very.” And, in fact, there is no way I would voluntarily swim in such waters. I knew of and felt the power of some Hawaiian myths, but remained a geeky haole (white person), quite afraid of sharks. I remember body surfing at a great place near Portlock place at Koko head with a crowd of others. As we waited for waves a fishing boat came by and warned us that they had just seen a shark. Everyone moved in closer to the break line, but after missing a wave or two moved back to where we could catch the waves. I was definitely fearful and on guard. True Hawaiians, on the other hand, were not all that afraid of sharks.

My uncle who had come to Hawaii a little prior to 1920 told a story he had heard about the time when dynamite had first come to the Islands. The Hawaiians would go to the outer reef in their canoes, set off a stick of dynamite under water, leap into the water and throw the stunned fish into their canoes. Sharks would show up and go into a feeding frenzy. The Hawaiians would pretty much ignore them except for an occasional push or kick and keep throwing fish into their canoes. I’m not sure how much of this I believe, but certainly the story has it that Hawaiians were very respectful, but not afraid of sharks. One must of course distinguish between reef sharks and the pelagic Tiger shark. Spear fishermen know that they should keep their speared fish at the end of a long line rather than tied to their waist because reef sharks would go after the speared fish. Actual shark attacks, on the other hand, seem to come from Tiger sharks who mostly can reach shore only where the reef is missing or not very wide.

My `aumakua experience of Hawaiian culture was a dream. Others have had vivid, waking experiences. On the Big Island of Hawaii where there are active volcanoes, there is a tradition of Madame Pele, the goddess who controls volcanoes. Many people native or otherwise believe that Madame Pele actually exists. She supposedly is fond of gin so people living near the volcano leave offerings of gin near their houses. It seems to be a good idea to be respectful and try to be in her good graces whether or not she really exists. My mother told me, probably in the 1970’s, of an older couple (haoles), friends of her and my dad, who happened to be in the parking lot of the Crater rim road at the Kilauea Iki view point during the great eruption of 1959. It was at night, but hardly dark, as a fountain of lava about a mile down the crater was illuminating the landscape. A mile sounds like a considerable distance. However, the lava fountain, on one occasion reached almost 1900 feet high (see Wikipedia). The Empire State building in Manhattan is 1454 feet high at its very tip top, while the new World Trade Center’s spire tops out at 1776 feet. So while my folk’s friends stood near the edge of the crater one can imagine a garish, flickering light, intense radiating heat, dark shadows and a loud roar as molten gobs of lava fell into the lava lake at the fountain’s edge. The couple took in the awesome scene for a while, then noticed a Hawaiian women nearby. She had reddish hair and wore a red holuku (Hawaiian mother Hubbard dress). They exchanged a few remarks with her about the incredible scene they were witnessing, then turned back to look at the fountain. Finally, satisfied, they turned to go back to their car and noticed the Hawaiian women rise a couple feet off the ground, drift away to the edge of the parking lot, and vanish.

When I heard this story, I felt a tensing of muscles in my back and my hair felt like it was standing on end. Could I have had this same experience? My emotions said so, but my reason said unlikely. The couple had an hallucination. But just what is the status of hallucinations? One notes that our entire experience of the world is entirely inside our heads, with considerable mental processing of our raw sense impressions. Could not the processing of neuronal pathways, influenced by one’s cultural background, and an incredible, dreamlike scene, construct an image that appears in consciousness as real? It would seem so. Hearing this story made me think that stories, for example, of the Greek gods were likely based on genuine hallucinations rather than simply literary imagination. Probably literary imagination was involved in the elaboration of such hallucinations into an entire cosmology, but behind the stories were experiences of the gods and goddesses that passed for real.

For the Hawaiians living before Captain Cook’s discovery, the myths were integrated into their natural surroundings and constituted an entire world view. Besides being the background to hard won practical knowledge and lore, the myths told of the place of humans in the universe. Their meaning carried religious significance, practical significance and social significance. In the modern world, West and East, reality has been split into “areas” and thereby degraded.

This post has gone on long enough and I will doubtless get later into an inquiry about the concept of “reality”. For now let me just say that if someone explains to you what “virtual reality” is all about, the proper reply is “I didn’t know there was any other kind.”

Spiritual Quest, 1953-1954

What compels one to sail on a spiritual journey? Fundamentally there is no real answer. It is a mystery similar to that arising when considering the question of why some people climb mountains. If someone who has no interest in mountains asks why I climb, I’m really at a loss to explain. It is obvious to me that often I feel more alive and full of joy on a mountain, seem to feel a sacredness in great mountains, seem to “see” further, and feel a sense of spiritual well-being and insight, indefinable in concrete terms. If a person is immune to such feelings, there is really nothing to be said that would give her or him a real, personal understanding of why one would feel compelled to climb a mountain.

As a child I was fortunate in having parents who were not conventionally religious. Neither ever went to church. There was no attempted brain washing. I was curious about religion and on one or two occasions actually went to Sunday school at Central Union Church in Honolulu. Sunday school there was obviously simply a place to harbor children while their parents were in church. Theology was conspicuously absent. No help there. Later, in high school, we had a Christian non-denominational chapel which I found exquisitely boring. I was already an unthinking atheist. So, later in life, when I felt the need for an understanding that was deeper than that provided by a scientific and humanistic education, I could approach the search, more or less unbiased by childhood experiences. I was open to any spirituality based on beliefs that seemed reasonable to a person who had unconsciously committed to a scientific world view.

In an earlier post I’ve already set out one criterion for my journey: it must be superstition-free and beliefs should not be based on their comfort level. Now, in the years after college as I worked as a mathematician in Pasadena for a branch of the Naval Ordinance Test Station, climbed and skied in the Sierra, and met the friend working on his Ph.D. in physics at Cal Tech, I gradually formed another criterion: Any spiritual outlook should be totally comfortable and compatible with a scientific world view. This is not to say that I thought a scientific world view the be all and end all of knowledge and life. I had heard about logical positivism in college and had taken it to claim (probably mistakenly) that the world of experience outside of science lacked meaning or validity. I felt that this view was ridiculous though I didn’t know enough about positivism to argue against it. I knew that I loved poetry, good poetry and kitchy bad poetry, was carried away by classical music, and felt impelled to try understand all of life, scientific and otherwise. Somewhere along the line I had run into the world of myth in Joseph Campbell’s books and found exciting his ideas about how myth gives meaning to life.

See http://www.amazon.com/Thousand-Faces-Collected-Joseph-Campbell/dp/1577315936/ref=sr_1_1?s=books&ie=UTF8&qid=1462321437&sr=1-1&keywords=joseph+campbell

Although I was captivated by the “worlds” outside of science, I decided that any religious claims that attempted to contradict the stories of the scientific world were unworthy of consideration as serious truth, spiritual or otherwise. At the time this left a big question in my mind. Was there already existing somewhere in all of mainstream world religion or in any existing sect, a spiritual path that satisfied the criteria I had developed?

For my Future Wife

Our relationship will never go to that completion I desire unless you are
as crazy as I am. Our human condition is to be trapped in an animal body
aspiring for the stars. Our consciousness non-existant for an eternity of
the past and to be non-existant for an eternity to come. Meanwhile, for a
brief instant we are here. If one truly realizes our condition one must
be crazy, at least by conventional standards. This is not a sick,
destructive craziness, but a creative, tragic, open and aware craziness.
This kind of craziness I’m talking about is the only sanity. Are you that
crazy? A humorous saying is, “Never sleep with anyone crazier than
yourself.” I would turn that around and say, “Never sleep with anyone who
isn’t as crazy as you are.” If one is in touch with another at that level,
nothing else matters; not differences of age, of personality, of
temperament, of wealth, of fame, or of position in society. If one
doesn’t have a deep bond at that level, the relationship may be nice but
will never be complete. And can never bear the name of true love.