Circle Triangle Square



Sengai Gibon (1750-1838) was a Japanese Zen master who was an artist. There are many stories about Sengai. One I particularly like shows his courage and compassion. The Daimyo, the high ranking Samurai who was the local ruler, loved chrysanthemums. The gardener’s dog destroyed some of his prized blooms and so naturally the gardener needed to die. Sengai leveled the rest of the flowers with is trusty scythe, presenting himself to the Daimyo the next day. Sengai asked to be killed for certainly in this area the farmers, who were dying of hunger were ignored by the Daimyo while pretty plants were valued above a human life.

The Daimyo got the message.

One of Sengai’s most famous works is “Circle Triangle Square.”


There are many interpretations of what this painting is about.

The inscription at the left alludes to Sengai’s temple, an ancient temple already at that time about 700 years old. it was the first Zen temple in Japan. So maybe the shapes refer to the temple. Or the pagoda at the temple.

Or maybe the inscription is not about the subject of the painting and it is just in effect his signature. Zen masters in Japan and before that China were often identified with and named after their monasteries or the mountains they lived on.

Or maybe the circle is the cushion (zafu) the meditator sits on, the triangle is the mediator with the top point as the head, the solid base the butt and crossed legs. The triangle and meditator as mountain (the triangle/meditator/mountain idea was suggested in conversations with sensai Maezen at Hazy Moon). The square might be the zabuton, the square pad the zafu sits on.

I would like to interpret it geometrically.

I have no idea how much geometry Sengai knew. Clearly basic geometric shapes interested him enough to paint them.

I already discussed the perfect symmetry of a circle in the post “Circle and Wave.” Recall that a circle is an idea, defined as that object that is equally distant at every point from a central point. This distance is the radius of the circle. So all it takes is a distance to make a circle. The circle has perfect rotational symmetry, without beginning or end. When that symmetry is broken, we saw that we can produce waves, and these waves define particles, the basis of form.


We saw that breaking the symmetry of the ideal circle led to waves, particles and the manifest universe of form and is embodied in the yin yang symbol.

So circles are amazing but where do squares and triangles come in? How do they relate to the unwinding of the perfect circle as a wave.

Lets start with how a square and triangle relate. A square is two triangles.


Next, how do circles and squares relate? There are many ways, but here is one I like: Every circle precisely defines two squares, each of which intersects with the circle at four points. One square is inside, the other outside the circle. In a perfect symmetry, every square likewise defines two circles, each circle intersecting with the square at four points:


Those then define two larger and smaller squares and circles ad infinitum.



Now, how do circles and triangles relate and how do they make waves?

We can think of the circle as a clock face. This time we will think of the radius as a minute hand, here pictured as arrows, but this minute hand will go counter-clockwise starting at the 3 o’clock position. We will see how high the tip of the arrow is above or below the horizontal line bisecting the circle at several points.



Next lets put each vertical line along a horizontal line with each clock hour marked, starting at 3 o’clock and going counterclockwise. Even with just a few straight lines we see a wave emerging:


In this figure we placed the vertical lines above and below the horizontal line at their clock positions in the circle as marked on the horizontal line and connected the tips of the arrows with lines and got a rough wave.

If we were to add so many arrows and vertical lines so that the circle is filled with lines and arrows we would get a perfectly smooth wave.

What is this wave?

Each arrow in the circle goes from the center to the circle itself and so all are the same length. Each is a radius of that circle. It also is the hypotenuse (the longest side) of a right triangle.

Here is one triangle isolated to show that they are each indeed a triangle:


This figure Shows one of the triangles defined by the arrow and the line from the tip of the arrow to the horizontal bisecting line.

Now, lets say the arrow/radius/hypotenuse is one unit. It doesn’t matter one unit of what. A unit could be one inch, one mile, one light year, one unit of 6.753 mm, one diameter of an oxygen atom, it doesn’t matter; are all kosher as long as all other measurements that relate to that unit length, say of the other sides of the triangle, are measured in a way that is related to that basic unit (in inches, miles light years, multiples of 6.753 mm, diameters of oxygen atoms).

Remember basic trigonometry: the sine of a right triangle is defined as the length of the side opposite an angle (other than the right angle) over (that is, divided by) the hypotenuse. It is a ratio, no units, they cancel, just a relationship that always holds. Since the arrow/hypotenuse/radius here is 1, we defined it as one unit, the far side across from the angle is the length of that side over one, so that side IS the sine for that triangle. Slide4Here we see a right triangle, the thick line is the side across from the marked angle. The diagonal line is the hypotenuse (the arrow in our circle). The thick line is the side across from the angle. To the right of the triangle we have the thick line divided by the diagonal hypotenuse (which is 1) = the thick line. The length of that line is the sine.

So we collected these sides of the triangles, these sines, which were the length of the tip of the arrow above or below the horizontal bisecting line, and we created a sine wave!

Circle, square.  Every square defines two circles, every circle defines two squares, without beginning or end.  Square triangle. Two triangles make a square. Circle triangle. Every circle is made up of the hypotenuse of triangle after triangles, and these define waves (we just looked at one such wave, the sine wave).

So do you think Sengai had any of this in mind? Did he know trigonometry? Did he intuit that these basic forms could describe all form? These objects that have no physical existence but are abstractions, the product of mind, empty of substance?


“Nevertheless this great ocean is neither a circle nor has directions. The wondrous features of this ocean that remain beyond our vision are inexhaustible…. It is just that as far as my vision reaches for the time being, it appears to be a circle.”



photo courtesy of Susan Levinson

Emptiness for Art Historians

All phenomenon arise because of ever changing causes and conditions.  Phenomenon include what we perceive as things and events. These causes and conditions will change because their energy, their momentum, will dissipate, and because they result in new causes and conditions, in an infinite feedback of changing conditions resulting in changing phenomenon resulting in changing causes and conditions resulting in changing phenomenon…..

No essence, no fixed meaning or substance.

Yet we reify with concepts. We try to freeze and categorize reality. We try to capture it so we can deal with it on our terms. When the convenient tool of language distorts our appreciation of reality it is a (sometimes subtle, sometimes not so subtle) form of delusion.

A painting or a photograph that attempts to render a scene, whether a landscape, still life or portrait is a frozen approximation.

It is not how the world is really experienced.

We scan a scene with our eyes, the constantly fluctuating light and movement creating an ever changing tableau we couldn’t possibly keep up with.  Movement is pieced together, time is knitted into a flowing substance in our brains. We project our memories expectations, hopes and fears on to a scene. We fill in the blanks left by our blind spot and poor peripheral vision and our limited perspectives with projections of what we think (or worse, hope) is there.

What you experience in the conscious mind, that is, the words you might say to yourself about a scene, or the efforts you might make as an artist trying to paint or photograph the scene to “capture” it, are the tip of the iceberg.  A third of your brain was used integrating and evaluating the energy changes your eyes sensed into a “coherent” narrative that became those words and perception and “conscious” awareness of the scene. Just the tip of the brain iceberg.

You reify the scene.

Western artists who are interested in rendering a scene have attempted to capture the ever changing barely imperceptible fluctuations of energy that are shared with total intimacy between what we classify out of convenience into perceived and perceiver to re-create a scene that in a sense never existed.

That’s why in a recent film “Tim’s Vermeer” they speculated on how the artist Vermeer got his effects with mirrors (magic is always done with mirrors!), gimmicks they say he needed because the human eye does not see a scene how he painted it. Whether they are right or not about his gimmicks, Vermeer’s genius was to transcend how we usually see and transcribe that visual experience on to a painted surface.


We understand as artists and as scientists that there are no “outlines;” they are a convention, an illusion. Edges have softness from being curved, from diffraction of light, from reflected light off surrounding surfaces bleeding into the shadows.So Leonardo Da Vinci invented sfumato.

Impressionists tried to capture the fleeting nature of perception. 400px-Claude_Monet,_Impression,_soleil_levantPointillists experimented with the nature of color perception.


Cubists tried to deconstruct how we see images, shifting our awareness over ever changing surfaces, particularly with movement.


But I think the best presentation of emptiness in the Western cannon is:


Emptiness and Form


In my post “Circle and Wave” I suggested an intimate relationship between the absolute symmetry of the circle and the broken symmetry of waves mathematically derived from circles, and a similarly intimate relationship between waves and particles. In my post defining energy I discussed how energy is not a substance, but rather energy is as elusive and hard to grasp as it is essential to the world of things that go bump, the world of experience. In my last post on sensation and perception I suggested however awesome the world of experience is dualistic and maybe we need to go deeper and review the Buddhist experience described as emptiness (well, what Zen masters assure us is experience, I make no personal claims; I am wading here into waters that are very deep, well over my Zen pay grade and all of my heads, Zen or otherwise).

Lets do it anyway. It’s fun stuff.

I am going to refer to two poems, the Heart Sutra and the Identity of The Relative and Absolute, that we chant at the Zen center (as they do in others) and since I chant it, I claim the right to explore it with the disclaimer I do so as a student, not a teacher.

In the Heart Sutra it is said (here dharmas means things/events; like particles and waves, movement with or without mass!):

“Form is emptiness, emptiness is form;

Sensation, conception discrimination, awareness are likewise like this.

O Shariputra all dharmas are forms of emptiness, not born, not destroyed;

Not stained, not pure, without loss, without gain;

So in emptiness there is no form, no sensation, conception, discrimination, awareness,

No eye ear, nose tongue body, mind;

No color sound, smell, taste, touch, phenomena;

No realm of sight.. no realm of consciousness;”

There is more to the Heart Sutra of course. The point here is, as sophisticated as we can get about contingencies and projections, about energy, about a universe of waves that are particles, particles that are waves, even getting deeper to a universe of no-thing, and every thing, just energy, we are still in a realm of concepts, we are still thinking about it. We are creating phantoms, chimeras of deep but still limited intellectual ideas and limited biological experience.

What is this emptiness that is form?

The rainbow is empty in a sense. There are no rainbow atoms, you can’t box it up and take it home with you. And yet it has form, at least in your brain. Not a bad start, especially for those of us of limited Zen chops. But emptiness in the Heart Sutra, in Buddhism, goes much deeper than that.

I don’t want to diminish emptiness in Buddhism by calling it an idea or a concept or by treating it as one. Nevertheless, allow me a bit of indulgence here. In Zen we don’t tend to go on about definitions. I am not a Zen teacher, and so I will share with you some definitions of emptiness. For the sake of discussion, and particularly since I am not qualified to define or describe emptiness, lets see how it is defined more or less academically:

In “An Introduction to Buddhism” by Paul Harvey, a textbook used in a course on Buddhism at UCLA, emptiness is variously said to be a lack of: fixed form, of Self, of separateness, of inherent existence or nature, of solidity, of permanence, of duality. And even emptiness is empty!

In “the Shambala Dictionary of Buddhism and Zen” emptiness, or shunyata in Sanskrit (sunnata in Pali, Ku in Japanese), it is suggested that since all composite things (form) are impermanent and devoid of independent lasting substance they are basically appearances. The article discusses Yogacara and Mahdyamika (two main philosophical schools on Buddhism) approaches to emptiness. In the Yogacara or “Mind only” school of Buddhism, since all is Mind, all is empty, just projections of Mind. This is clearly consistent with the quotes I gave above from Biocentrism and the Lankavatara sutra. The Lankavatara sutra is indeed considered a text of the Yogacara school and was favored by early Zen masters in China. Biocentrism is clearly treading that same path. In the Mahdyamika school of Nargarjuna there is thesis of two truths: 1. the conventional or apparent truth that seems real is an illusion because all things interdependently arise (that web of interactions again) and 2. the absolute truth, the emptiness beyond existence and non-existence that can only be directly experienced.

In “The Princeton Dictionary of Buddhism” by Buswell and Lopez emptiness is said to refer to the truth of suffering (first of the four “noble” truths) in early Buddhist texts, as both relate to impermanence. But somehow it also alluded to the absence of cleanliness, which is far from what the Heart Sutra is about. Their article pointed out that it is with the Mahdyamika school of Nagarjuna that emptiness was considered to relate to the entire universe. Because all things arise dependently, they lack, or are empty of, an intrinsic nature characterized by independence and autonomy. In the Mind only Yogacara school they say emptiness is the lack of subject or object. That is, no inside and no outside; nonduality, just Mind.

In his translation of the Heart Sutra (p 68) Red Pine points out, referring I think to the same dependent arising as Buswell and Lopez alluded to in their discussion of the Mahdyamika school and emptiness, that “nothing exists by itself, that any given entity can only be defined in terms of other entities in time, space and mind, and these in turn can only be defined in terms of other entities, and so on, ad infinitum.” Red Pine goes on to say that emptiness, however, is not nothingness, it is “the absence of erroneous distinctions that divide one entity from another, one being from another, one thought from another. He concludes emptiness is “not nothing, it is everything.” Later (P 75) Red Pine speaks of 5 kinds of emptiness that Buddhist commentators referred to, but for the Heart Sutra the most important was emptiness of self-existence. Form is empty of anything that be called self existence as whatever we use to define form is dependent on something else. But emptiness is form! He quotes Nagarjuna: because of emptiness, all things are possible. And Ming-Kuang: Form and the mind are not different… The mind is not outside or inside or in between. (P78)

We have seen that all that happens, all we perceive, from a scientific point of view one could say that all that exists, consists of energy transformations. And yet energy itself is not a substance, but only that which makes all things happen. In fact, energy can not be measured directly but only as changes reflected in what happens. This is a lot like Red Pine’s circular ad infinitum of any entity being defined only in terms of other entities (or phenomena).

Certainly we have seen that solidity is an illusion or, at best, an epiphenomenon of quantum mechanics. Like rainbows. Phantoms, projections.

All we perceive and can know with our brains is just shifts in energy levels.

As much as I have tried to stay away from making science/Buddhism connections, maybe indeed science is approaching an understanding of emptiness.

Maybe it isn’t so hard to see from the scientific viewpoint that there is no fixed unchanging center, that form, which I take to be that which can be perceived, that which interacts, that which is measured when energy changes, is not a persistent brute fact of what there “is,” but rather a manifestation of the ever-changing energy transformations, each change depending on the other and every change that ever occurred and ever will occur, of the constant movement of things that have no inherent fixed existence.

And if we take non-dualism as given, how much less can we see any separation that is meaningful and inherent.

This is the opposite of Platonism, which some mathematicians and physicists think is the way things are. In Platonism there is an ideal world of perfect forms, and we can only see their imperfect reflections in our world. Or we can discover them with mathematics and concepts and ideas and ideals.

But in Buddhism there are no concepts or ideals out there to strive after. We make that stuff up, that is just more chimeras, more phantoms.


In Buddhism we are not approaching some perfect world of form, but rather form is born of a web of interactions and is a manifestation of Mind. There is no True Absolute Eternal Form to be sought after, just constant movement, constant rising and falling, coming together and parting.


Entertainers on a Samurai boat in Tokyo Harbor. Photograph by Susan Levinson.

And it is emptiness that is pregnant with creativity, that allows the flexibility, the pirouette of the dance of form, which is the dance of Mind.

What is perceived, form, is not solid, some inherent eternal quality of stuff, but just perhaps for mind to be at play, to frolic, emptiness takes form.

Now, form may be empty of inherent existence, a manifestation of Mind, but when you drop that rock make sure your foot isn’t in the way! Even the Buddha died, some say of bad meat. Seems a bit like poor form.

So why explore symmetries, waves and particles, why look into energy, sensation and perception, even quantum mechanics?

Because we are here. Because this is the manifest Universe. It is not outside the Dharma (Dharma means here teachings of Buddhism or more generally, Truth, when spelled with upper case “D”).

At the Zen center we chant the Zen poem, the “Identity of the Relative and Absolute.” The IDENTITY; not the subservience of perception, of energy, of the relative, to the absolute.

The Zen master poet Shih T’ou Hsi-chien ( Sekito Kisen in Japanese) in the poem warned us over a thousand years ago:

“To be attached to things is illusion;

To encounter the absolute is not yet enlightenment.”

He explains:

“Each and all the subjective and objective spheres are related,

And at the same time independent.

Related but working differently, though each keeps its own place.”

And later he adds:

“Each thing has its own intrinsic value and is

Related to everything else in function and position

Ordinary life fits the absolute as a box and its lid.”

The universe of energy patterns and change is the relative. Ordinary life. And the relative, our life, is intimately related to the absolute, to the non-dual, to Mind, to emptiness, to what can not be grasped by the senses or the intellect, but may be directly experienced according to the Zen masters, like “the foot before and the foot behind in walking.”

Once again, my ignorance and lack of Zen chops. I can not explain it any better. I can not convey experiences I have not had.

But that is what the Master Zen poets tell us.

Maybe this extraordinary practice, this deep and splendiferous vision beyond visions, these experiences beyond grasping and our intellect, our lives, are as Nyogen Roshi says:


 30 Kushan Buddha

Energy, Sensation, Perception


Sensation and perception are how we seem to experience the world. Practitioners of Buddhism and science have given a lot of attention to how we do that and what it means.

From the scientific viewpoint, sensation occurs when a specialized organ interacts with the form of energy it evolved to interact with. These specialized organs are the sensory receptors in the eye, ear, nose, skin, or tongue, for example, though animals have a large array of receptors, like infrared receptors in pit vipers or sonar in bats.

And in an inspired insight I particularly admire, in Buddhism the brain is also a sense organ, one that “perceives” both sensory inputs from other sense organs but also you might consider thoughts a sensory input.

The way it works it that when the receptor receives energy that is in a form that specific molecules in the receptor can interact with (photons with photoreceptors in the eye, chemicals that interact with receptors in the nose or tongue) this changes the energy state of the receptor molecules. The increased energy changes the form and position of the receptor molecules, even if very slightly, that is, there is molecular movement. Atoms in the receptor molecules are now in different orientations relative to each other, stresses are made in chemical bonds, chemical bonds may break and new bonds form. That results in a cascade of further energy transformations that results in a signal that something has been sensed. In higher animals, the signal is transmitted by nerves to the brain, and then the brain sends signals around to different parts of itself (called associative areas; an aspect of the brain as sense organ) organizing the sensory inputs into perceptions and then thoughts or discriminations about those perceptions.

What we sense and perceive then is changes in energy: changes in light (electromagnetic energy) with vision, air pressure (the kinetic energy of gasses in the atmosphere impacting on our ear drums) with hearing, chemical energy with taste and smelling, kinetic energy of molecules with touch (pressure, temperature and pain), electrochemical energy in our brains with thinking.

Yes, even thinking is movement. What moves when thinking happens? Lots of things. Neurotransmitters move across synapses, responding to moving charged energy fields, fields that are created by charged atoms (sodium, chloride, potassium, calcium) flowing in and out of nerve cells, themselves responding to changes in the nerve created by other neurotransmitters).

Thoughts are no different from other perceptions, or for that matter any other event in time and space:

It really is all energy transformations.

Sensation and what we do with it is a major theme of Buddhist thought, and is also inherent in the scientific program. It is how we gather the data that makes up Scientific Truth. It is how we navigate through our day-to-day lives.

We may rightly ask: What is it, who is it, that senses, that perceives? In a non-dualistic universe, what does it mean when we refer to an internal and external, to conditions, energy relationships, sensation and Mind (see also Doman’s post “Meditation”).

And Zen is not alone in asking such questions:

“I say that, as soon as I conceive a piece of matter or a corporeal substance, I feel myself necessarily compelled to conceive along with it, that it is bounded, and has this or that shape, that in relation to some other body it is either small or large; that it is in this or that place, and in this or that time; that it is in motion or at rest; that it either touches or does not touch some other body; and that it is one, few, or many; nor can I separate it from these states by any act of the imagination. But I do not feel my mind forced to conceive it as necessarily accompanied by such states as being white or red, bitter or sweet, noisy or quiet, or having a nice or nasty smell. On the contrary, if we were not guided by our senses, thinking or imagining would probably never arrive at them by themselves. This is why I think that, as far as concerns the object in which these tastes, smells, colours, etc appear to reside, they are nothing other than mere names, and they have their location only in the sentient body. Consequently, if the living being were removed, all these qualities would disappear and be annihilated.” (Galileo Galilei 1623, pages 196- 197)


Robert Lanza and me at the Hazy Moon Zen Center

“First Principle of Biocentrism: What we perceive as reality is a process that involves our consciousness.” (from the book “Biocentrism” by Robert Lanza, MD)

“Second principle of Biocentrism: Our external and internal perceptions are inextricably intertwined. They are different sides of the same coin and cannot be separated.” (Biocentrism)

The importance of conditions, both internal and external (ultimately these are only terms of convenience) and how we perceive and so understand the world is central to Buddhism as well. The view of the Western scientists Galileo and Lanza (Biocentrism) is not so very different from what we find in the Lankavatara Sutra, a foundational Zen text that is over 1600 years old:

“perceiving consciousness, .. is the result if imperceptible habit-energy and imperceptible transformations, while object-projecting consciousness is the result of grasping different phenomenon and the habit-energy of beginningless projections.”

“who see things as devoid of self existence, as clouds in the sky.. as illusions or mirages or dreams or moonlight on water, and-regardless of whether they appear to be inside or outside the mind as projections from the beginningless past and as not existing apart from one’s own mind. “

“Blue and red and every color/milk and sugar and conch shells/fragrances and fruits and flowers/the sun the moon and light Like the great ocean and its waves/are neither separate nor not separate/…[but] rise together with the mind”

“existence and non-existence are perceptions of one’s own mind”

“The world of objects that are perceptions of one’s own mind are fabricated and manifested from one’s own projections. They change and disappear every moment, like a river or a seed or a candle of the wind or a cloud… impelled by habit-energy without beginning”

“..all things are characterized by two types of conditions: namely, internal and external.”

“The application of conditions results in a rug from yarn, a mat from grass, a sprout form a seed, and butter from milk. These are the before and after results from external conditions.”

“As for internal conditions, such things as ignorance, desire and karma constitute the conditions,….. give rise to constitute the conditions. They aren’t separate”

[Lankavatara Sutra, Red Pine translator]

When I shared these quotes with Bob Lanza some time ago he commented that he was surprised that the ancients could grasp this without science. I told him I was surprised he thought he was actually grasping this with science! I think it comes from a place of deeper understanding. That’s why Bob wrote “Biocentrism,” and most scientists could not or would not.

We project ourselves on an “out there” and “in here” of energy transformations.

Lets look at some examples that are easier to grasp and at least give a bit of a feel for projections.

Here’s your blind spot. Close your right eye and look at the x with the left eye. Bring the page in and out and you will see the B disappear if you are really holding you eye on the x (at first it may flicker in and out if you tend to move your eye).


          B                                                     X


Now look around. Any blind spot? Anything missing? Nope. You project the world into your blind spot. You do this all the time. Most of what you see from your “peripheral” vision is based on clues and expectations; your peripheral vision is really poor. Your brain stitches a full seen together.


Take the color yellow. You may think that yellow is a primary color (it is for paint, not light), that it represents a specific frequency of electromagnetic waves in the visible spectrum that is always “truly” yellow when you see something as yellow. But you don’t see yellow. Ever. Your eyes, the photoreceptors in your retina, have no ability to register wavelengths that would be “yellow” light. Your eyes, in effect, deconstruct the light by registering the electromagnetic energy in photoreceptors that are sensitive to what we consider green and red. You brain puts that together as yellow. In fact, yellow is not a primary color on your computer screen, your high-definition television? Pixels of red and green. Not yellow. Put on the color palette of your computer (say in Photoshop or Powerpoint) and see for yourself! You make yellow form green and red.

You project yellow “out there”. Yellow! It is only in your brain, it is not your eye, that yellow exists.


Is there a rainbow “out there”?

No; a rainbow does not exist.

An infinite number of rainbows exist for you if you are at the right place at the right time. When the conditions are right. And these conditions include a perceiver. Otherwise a rainbow does not exist, there is electromagnetic radiation (light), water and air; an infinite number of potential rainbows, but no rainbow.

images-3 images-4



A ray of light (let’s accept for the moment there is such a thing as a ray of light) hits a relatively spherical droplet of water in the air. The light entering the droplet is bent, refracted, the drop acting like a lens. That’s what happens to light when it goes from a less dense to a more dense material, say air to water (or to the plastic in your spectacles). That is how lenses work, and is called refraction. The higher the energy of the light, say blue light compared to red light, the more the light bends. While most of the light would just go on through the transparent water droplet, there is an angle at which light going from a denser to less dense material is bent so much that it is “internally reflected”. When this happens to light that had entered a water droplet at this critical angle is reflected and that light, now separated into different wavelengths by refraction, can reach your eye. The light rays coming out of the droplet are spread out according to how much they bent and that was based on their energy. Depending on where you are compared to that droplet and to the adjacent droplets determines which energy rays you see.

When the conditions are just right, you will see a series of rays with a range of energies from different droplets, deconstructing white light, unmasking an array of visible light that was there but not visible until the energies were manipulated, a bit ike prisms, and that series of rays of light of different energies will be seen as different colors. That is what that you perceive as a rainbow. Move a bit and you will see new rays from other droplets, a new rainbow. But there never was anything that is a rainbow. Light of different energies  enters your eye then is perceived in your brain.


Water, light, mind, but only in a very specific relationship; other than the relationship, no rainbow. Conditions change ever so slightly, you move, and it is gone. Same light, same water droplets, different angle, no rainbow. It’s not a “thing” in the sense that you can’t put it in a bottle. You can perceive it. You can experience it. Your dog can’t, she doesn’t have the ability to see all of the colors; no rainbow for her. A rainbow is real but totally contingent on just the right conditions, including your mind. Your mind gives it color. When the conditions changes, the earth rotates so the sun is at a different angle, the wind disperses the water droplets, your attention is diverted, the rainbow ceases to exist.


Clouds are much like this as well. Clouds are water droplets made visible due to light scattering by water droplets existing in the air at sufficient density and change at each moment depending, evolving, appearing and disappearing depending on the air temperature pressure and the density of the water dispersed in the air. The rainbow and the cloud, each is an event made up of light and water droplets in the sky, and these events do not exist as rainbow or cloud other than your perception of them, your experience of them. The rainbow and the cloud are projections of our minds.

Certainly it is easy to see, for example, that a rainbow doesn’t exist outside of a special relationship between an eye, a brain behind that eye, and droplets of water reflecting light at just the right angle. All have to be aligned and all contingencies in place for there to be the transient phenomenon we call a rainbow. There is no object, no thing you can grasp that is a rainbow outside of these contingencies, these “dependent arisings” to adapt some Buddhist terminology (the term is usually used less concretely).

So, is reality described completely and essentially by energy transformations and what your brain cobbles together, based on conditioning, evolution, ever shifting contingencies and dependent arising, one thing leading to another?

No, I don’t think so.

Seems deep, but still dualistic.

Still ideas and concepts.

Maybe we can go deeper.

Maybe we should consider what Buddhists refer to as emptiness.



Love and Marriage







Biologic imperatives

Expectations, voiced or not

Innocence lost, innocence gained

How close is too close, how much is too much?

Not understanding, understanding

Different worlds, same world

Why do I want to be angry?

Glorious and amazing

Wishful thinking






Guan Yin (Kannon in Japanese) , Bodhisattva of compassion, in female form. The male form was originally named Avolikiteshvara. She is the “hearer;” she hears the cries of all suffering, and will go down to the pits of hell gladly when she is called.

After 41 years of marriage to a woman I love, that’s about the only way I can understand it or express it, with poetry. And I rarely write poetry.

I doubt this is gender specific or sexual orientation specific from what I can see. And there are many relationships that are long-term and loving that I imagine do not encompass many of these things. This is simply what spilled out of me about my 44 years of a committed relationship with a woman I love as best as I know how.

I’ll come up with other poems about other relationships.

The real point is that I suspect there is something very deep and profound that these impressions of my life in love and in marriage circle around, that even the most solid day-to-day love can only approach or maybe only dimly reflect as long as egos and agendas are involved:

A love beyond conditioning and expectations.

Abiding compassion.

I think that is the flavor of Xin, the heart of Mind, the taste of existence.

And it doesn’t get old.

A Second Peek at Quantum Mechanics: The Double Slit Experiment


The double slit experiment is justifiably considered among the most simple, elegant and profound experiments in science.

In this experiment, we show first that light acts like a wave. This was first done two hundred years ago.

To see this you need to know that waves in the same place interact by adding up together. This is called “interference.”

If you take the peak, or crest, (the highest part) of one wave and add it to the peak of another wave, that is, if both waves (whether water or light or a mathematical wave on paper or in computer bits) are in the same place, you get a peak that is the sum of both waves. That is, the combined peak is as tall as both wave peaks added together. If the two waves are the same size it is like adding +1 + 1 to get +2. Similarly the troughs (the lowest part also add up to get deeper troughs, like adding -1 and -1 to get -2. So add two waves of the same size in the same place, perfectly aligned, and you get a wave that is twice as big (both peak and trough).

If you add the peak of one wave to the trough of a wave of the same size aligned in the same spot, they cancel each other out.  Adding the peak and trough of waves of the same size that are aligned peak to trough, it is like adding +1 (the peak) and -1 (the trough) to get 0.

There are also times where there are in between parts of the wave or waves of different sizes where the + and – numbers may not be the same, or cases where waves of the same size  are not exactly lined up. In fact it gets quite complex and to do it right you need calculus (Fourier analysis). A simple example is shown in the image below. The red wave is what we would measure or  “see” (say if these were visible light waves, or hear if they were sound waves) by adding the two smaller gray waves. this may be easiest to see where the two grey waves cross in the middle of the illustration; that point in the center where the gray waves cross is half the height of the red wave at that location.




So waves in the same place add up (constructive interference) or subtract from one another (destructive interference).

The set up for the double slit experiment  is a board with two small slits. Send a light through only one of the slits, and you will see the light in a pretty discreet area approximating the slit on the wall opposite the slit. Same would happen if you send light only through the other slit. Like a flashlight through a window. Now open both slits. You get a pattern of bars of light and dark because waves from the two slits interact. Where crests of the two waves hit the wall at the same time, they add up to a bright spot. Where the crest of one wave and the trough of the other wave lines up they cancel each other out.



This image shows how the series of waves wave to the left hits the wall and then part of the waves go through each slit. After going through the slits the waves radiate out in ever larger concentric circles, the two now expanding waves overlapping as they progress to the right.


In this  schematic we are looking down on the experiment, with the peaks of the complex wave on the right labelled “wave intensity” indicating where the peaks of the two expanding waves overlap after passing through the two slits and would be seen as bright areas on the wall opposite. Note that the brightest, or highest, peak is in the middle of the area labelled “wave intensity.” This highest/brightest peak is BETWEEN the areas of the wall opposite the two slits. This is exceedingly strange in that when allowing light to go through either one slit or the other, this area would have had little light.  The light from the individual open slit would have been either to the right or left of this central area, across from whichever single open slit the light went through.  This is like shining flashlights through each of two windows and finding the brightest light on the opposite wall not across from each of the windows but between the spots on the wall where the light from each window would hit the wall. This drives home show different light coming from two slits is from just combining light from two slits. It really can only be explained in terms of waves.


This image shows what you see in an actual experiment using red laser light. The top image is what you see with one slit open,the slit to the right,  a somewhat smeared out single spot. The bottom image shows the interference pattern with the two slits open, again with the brightest spot in the middle and other spots extending way to the right and left of where the light was from the individual open slit.

Now, light is also a particle.

If you send one photon (the smallest discrete unit of light) at a time through a double slit and have a VERY sensitive device  opposite the slits that will register one photon at a time, you will see individual pings, individual particles, in discreet areas. If you have one slit open, the pings will be all in the area opposite that slit. Open both slits and you still just see individual pings, but over time they will form the same interference pattern as the waves of light did. Of course the waves of light were made up of vast numbers of photons, but sure, they could in aggregate act as waves; maybe each has “waviness” that becomes a property of the whole when they are together like that. Maybe it is an “emergent” phenomenon of vast numbers of photons interacting.

Nope. We can send one photon or other particle (or atom or even collection of atoms) through the slits at a time and see that isn’t true.






In the top image we see schematically one green particle (atom or photon or “Bucky ball” molecule of dozens of carbon atoms) is going through at a time through two slits. Again, we would expect, if they are like little pellets, to result in a pattern we see here with two bars indicating that the pellets hit the screen opposite the slit they went through. But what happens is that over time they form the interference pattern just like a wave would even though one particle at a time went through one or the other slit. Note that in the lower image the bands start with random appearing dots but a patter evolves over time (and we see bands here that are oriented horizontally; just make it vertical in your mind if that confuses you; if it were the experiment with the green pellets/particles these bands would be vertical of course; or you can picture one horizontal slit above the other instead of next to each other. I’ll update this later with better diagrams) In panel a there are a few seemingly randomly placed white”hits” on the detector (here the photons register ass white against the black background). Similarly in b there is little to no pattern yet despite hundreds of hits. But c-e show increasing refinement of the pattern and loss of apparent randomness.

Here is the really cool part. The part that has physicists, mystics, Zen teachers and philosophers buzzing. It doesn’t matter how much later the next particle (or atom or molecule) goes through. Or when then the next one after that goes through. You can wait an hour or a year between particles if you are patient enough. And they don’t form the pattern in a way that is predetermined. Each time the order and location of the individual pings will be different: just where the first, and second, and trillionth particle lands won’t be the same in subsequent trials, but however random it seems, they will land so that the wave interference pattern forms.

Like with our spin L and R adding up to no horizontal spin over time when we send U or D particles along in the post of our first peek at quantum mechanics, we again see that our idea of time space and object permanency is a bit, really quite a bit, off. Where does the pattern reside?  How does an abstract mathematical function, a wave, translate into the behavior of particles, which themselves are energy patterns? How does each particle “know” where it is needed to be to keep the pattern?

It even gets better. If you measure, in any subtle way, which particles go through which slit, you lose the wave interference pattern. The act of observing changes it! The magic is gone, the particles lose their “memory.”

Physicists have been debating for a hundred years what this means. For now, let us just savor it.


(PS I will keep working on this to make it clear as I can with more illustrations and less repeating, but I thought worth getting it down and seeing what is clear and what isn’t to people)



For Father’s Day: Is that so?


I was writing a story riffing on a tale about the great Japanese Zen reformer and artist of the 18th century, Hakuin.

It seems a young unmarried women had a baby and wouldn’t give up the name the father. Finally she said it was the monk Hakuin. The parents were incensed, not only because he was a monk who was just starting out renovating a small, run-down old temple, but also because they had been supporting him in his endeavors.

They brought him the baby and said, here, it’s yours.

“Is that so?” He responded, and he took care of the baby.

A year later the young woman confessed that Hakuin wasn’t the father, so her parents went back to Hakuin, tails between their legs, and let him know the baby wasn’t his.

Giving the baby back he responded:

“Is that so?”



Nyogen Roshi told me Maezumi Roshi told him it may have been about someone else, not the well-known Hakuin. Maybe, but it’s just a story, right? I am still looking but haven’t seen this one in his autobiography or his student Torei’s biography (so far; I’m still looking) of Hakuin. Of course although there is a lot of material available in English, not all of Hakuin’s writings have been translated.  A recent memoir (Hitch-hiking with Larry David) ascribes the story to another Zen monk.

In fact, it is clear Hakuin enjoyed a good story. If you read Waddell’s translations of Hakuin there are all sorts of footnotes where it seems Hakuin just made things up. Hakuin even called one of his works “Tale of a Trip on a Night Boat” which was a phrase for bullshitting (it comes from a story about a peasant who said he had visited Kyoto, but when asked about a boat trip on a river there he came up with a whole river boat adventure despite that the river in question was not one of Kyoto’s real rivers but a small creek. No night boat soirees! He was caught in his lie!).

Hakuin was pretty funny. In one work of art he is smoking a pipe and the curling plume of smoke becomes him in drag as a folk figure of an older woman prostitute. He also cared. He made efforts to broaden Zen to a lay audience and wrote to his more powerful students that they shouldn’t over-tax the poor. I love this guy.




So then why would he take the baby? Wasn’t he complicit in a lie? Was he just a bleeding heart liberal? The obvious interpretation I often hear is that he was so non-attached he just took on whatever was in front of him. That may be true, but I don’t think that’s quite it. That view of non-attachment can get quite out of hand. I have heard that some Zen students (though none I know) think a great Zen master would be so non-attached he or she wouldn’t discriminate between a rock and a potato. That’s just dumb of course. And that certainly wasn’t Hakuin! He had a sense of humor, played the board game Go, was an artist, cared about the poor, bitched about stupid Zen people who thought because they had an enlightenment experience of some sort everything they did was cool. Hakuin shook things up. He discriminated plenty. He wasn’t biting into any rocks and he didn’t start an orphanage as far as I know.

But for whatever reason his practice and samadhi, his insight and penetration, led to ”is that so?” in that instance.

I appreciate this “is that so?” in another way.

I am always asking “is that so;” aren’t you?

Whatever my fevered brain projects, whatever I think that I understand, my fears and hopes and desires, whatever my senses present or presents to my senses, whatever phantoms and chimeras I piece together, isn’t “is that so?” a good question? Of course not in so many words, and usually not consciously, but isn’t that pretty basic?

Even more basically, delusion aside, isn’t it just the Great Question of Existence, of life and death? Isn’t “is that so” the question of each moment, the question that is always being answered in the moment?

Why a question and not a declarative “that’s so”? I don’t know, but for me it just kind of usually is. Maybe it is my ignorance. But seems like sometimes it was like that for Hakuin too. Maybe sometimes he answered: “that’s so.” Maybe even sometimes just: “So”! I wouldn’t put it past him. But I just made that up.

I am not Hakuin, so go ask him for yourself if you can. I’m just saying “is that so” goes much deeper than passive acceptance. It is the sound of practice; it is the sound of the entire cosmos evolving in each moment.

As far as accepting the baby that wasn’t “really his,” don’t we always do that even if the baby is “ours” (i.e. meaning our eggs or sperm or we have kosher legal adoption papers)? Who knows what they are really getting themselves into? What does it means to be “ours” in any case? How do you own anything in this ever-changing cosmos?

For that matter, aren’t we always taking each other on, sangha, at work, at play, in the world? Like it or not, legal papers or not? Maybe we are all Hakuin and Hakuin’s baby both.

I think that’s so.

In classical Buddhism it is taught we have all been each other’s father, mother, baby, sibling, lover, friend, enemy, every relationship you can name again and again, time and time again, lifetime after lifetime.

Happy father’s day.






Behind the Curtain; A First Peek into Quantum Weirdness




Quantum mechanics grabs the attention of so many people for some good reasons.

Quantum mechanics deals in the atomic and subatomic realms. In the reductive scientific program it is about as small and basic as you can go based on actual experiments.

The results of these studies have led to highly reproducible observations and measurements.

These findings have led to technologic breakthroughs.

 And because quantum mechanics is counterintuitive, bizarre and no matter how hard you try to picture it, model it in your head, think it through, intellectualize, fit in into your daily four-dimensional experience of reality, you will fail, like thousand upon thousands of great minds have failed for a hundred years.

Let me start with an example. I will give others in future posts.

Lets say we are going to measure whether someone is standing upright, and call standing with her head up U for up and standing on her head (head down) D for down.

She could also be lying down, with her head to the left L would be measured and with her head to the right R would be measured.

We will assume for now those are the only four choices. Yes, she can be off angle, and we could deal with that with simple trigonometry, but it adds nothing to our understanding for now. Off angle measurements will come up later though, it is better not get sidetracked with that at this point. Lets savor the incredible weirdness first.

Now, say we can’t see her, but we have a device that if we align it upright to measure whether or not she is standing it will report U or D, reflecting whether she is standing upright head up (U) or if she is upside down standing on her head (D).

If we align the device horizontally it will also report R or L reflecting whether she is lying with her head to the right or left respectively.

We can only measure U and D or L and R at one measurement depending how our device is oriented.

Also assume once measured, she stays in that position until a measurement in a different orientation of the device is made.

So say we both have our devices aligned upright and you measure U so I know she is standing upright, and indeed that is what I get when I measure her position with my device after you made your measurement. It is as we expected. We both get U. She is standing upright, head up, feet on the ground.

 Now, you would expect that if you measured with your device aligned for standing and you get U indicating that she is upright I would measure neither R nor L if I aligned my device horizontally for lying down. I mean, after all, the person is upright, which is the opposite of lying down. It is 90 degrees away! Nothing overlapping here, standing up versus lying down, we have a clear dichotomy.

Indeed that is what should happen for people-size devices and measured objects. Say the way I knew whether the person was lying down was to look for her head or her  a couple of feet to either side of her belly button. If I find the head to the left, feet to the right, it tells me that she is lying down and in the L direction (head left). But if she is standing (whether on her feet or head) I wouldn’t find the head or her feet off-center, they would only be off to the left or right if she is lying down! No feet or head off to either side when the person is standing, whether upright or upside down. I should get nothing (zero), no R or L going on, when measuring the lying down aspect of her position.

And that is true for measuring the position of the person. Get a measurement with the first device that she is standing, whether on her feet or head, and then you won’t get a measurement indicating that she is lying down when you measure with the second Device. These are mutually exclusive measurements.

But in the quantum world it is different.

If you measure a subatomic particle as standing (meaning, say, measuring the particle’s polarization or spin, characteristics of particles that do have direction that can be U or D, L or R) and you get a U or D indicating the particle is say spin up or down, when I measure it’s lying down/horizontal position (again, whether spin or polarization, for example) with the second device I DO get a R or L!!!!

It is standing AND lying down? It is spin up and spin to the horizontal?

And even weirder, if we repeat this a bunch of times, when you send me a series of U particles I get a series of  R’s and L’s in the horizontal direction:

Y0u send me a series of U’s and I may get:

R, R, L, R, L, L, L, R, L, R, L, R, R, R, L, L, L, R, L, R, R, etc.

And if you do it enough times, like heads and tails in a fair coin toss, the total number of R’s and L’s will be the same for the series of U particles, they in effect cancel each other out, meaning the AVERAGE horizontal position is zero in the upright particle!

So, how do upright particles give a horizontal answer in the quantum world? And how does the “system” that includes repeated measurements know to average out the results over time? Where in the universe does the “memory” of previous measurements reside so it “knows” to average out to 0, to no “net” horizontal spin in the spin up electron system (or no net horizontal polarization in the vertical polarized photon)?

If you say it is in the property of the electron or photon, then where is this property residing in these fundamental particles? How does a new particle know the property of the last particle? Or of the particle measured a second or hour ago, a billion years or a trillion particles ago?

If you say it is a property of the system of measurement, it may be that could true, but again, where and how so? Where are these properties “written” how are they stored?

There are mathematical and experimental reasons to think that indeed it is not  a matter of such “hidden variables,” and later that may be worth exploring, but even just conceptually, where could they be hidden and how would the next particle know where to find them?

Kind of screws a bit with any mental picture you may have of time and space and what a fundamental thing is, doesn’t it?


Keep It Simple (!)



Granted I have not kept it simple, and since in later posts I plan to discuss things like fields and quantum mechanics, philosophy of mind and time, and other things and concepts that our brains tinker with, I will  put up a simple post.


The best teachings I know of on how to live your life are:

      Pay attention

     No self-deception.


The truth of how it works in time and space:

     Everything that ever happened and ever will conspires to make this moment.


The truth beyond what ever happened and ever will:

      I don’t know.


photos courtesy of Susan Levinson



Defining Energy


The palpable universe and how we perceive it and know about it is all about transformation of energy (see also the post “Change and Suffering, Phantoms and Dreams”).

Energy patterns upon energy patterns.

We know energy is fundamental. Besides our intuition and use of the word very freely in common parlance, everyone knows that Einstein informed us that things are convertible to energy and energy to things:


E= energy, M= mass, c= the speed of light. Since c (the speed of light) squared is a constant, just a number that doesn’t change but makes the units work out:

Energy IS mass (stuff/things). Mass IS energy.

But you knew that part of the equation, probably since you were a kid. The other part of the equation Einstein wrote that you may not know addresses energy for particles that don’t have mass, like photons, and involves their momentum.

Momentum is how much oomph something has. The oomph it has when it interacts with something else.

For things with mass, like cars and people, momentum is mass time velocity. Velocity is the rate of change of position [speed] and direction. A big thing moving fast right at you has more momentum than a small thing moving slow-moving obliquely to you that will hit you with a glancing blow.

But photons, particles of light, as well as some other particles, have no mass, but have energy. They have oomph, they have momentum. Massless entities, things without thingy-ness, without substance, ghosts as it were, without form, can interact with massive entities with thingy-ness, form and substance.  Photons respond to the force of gravity. They can kick electrons out of atoms under the right conditions. They can get your atoms and molecules moving (resulting in increased temperature). They can cause chemical bonds to break if the photons are energetic enough (x rays and gamma rays are made up of photons); think radiation sickness, mutations and cancer! Their energy can be transformed into other forms of energy; think solar energy, where energy in photons from the sun is transformed into electrical energy (the movement of charged particles like electrons).

But still, Einstein’s famous formula of general relativity notwithstanding, what IS Energy?

“Energy is one of the most important concepts in science… Yet we cannot give a simple general definition of energy in only a few words.” “..we could define energy in the usual way as “the ability to do work”. This simple definition is not very precise, nor is it valid for all types of energy.” [University Physics for Scientists and Engineers Giancoli 2000 pg 155-156]:

“There is a fact, or if you wish a law, ….the conservation of energy. It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete, it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.

It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount…. It is an abstract thing in that it does not tell us the mechanisms or the reasons for the various formulas. “[His italics][Richard Feynman Lectures on Physics [4-1, 4-2]

So is energy anything is science? Is it just a placeholder, an accounting trick?

Kind of!

Energy is not a substance we can measure directly. You can’t scoop out a handful of it and smell it, touch it, weigh it. You can’t put a measuring stick into the universe’s gas tank to see how empty or full it is. It is probably infinite anyway, so no dipstick can serve!

The energy in the universe is certainly vast (well, if infinite, that is an understatement).

To give an example, there are particles that pop into and out of existence so rapidly we can’t measure them directly, we can’t use them to do anything useful but we can measure their effects indirectly. More on these in later posts on quantum mechanics and cosmology. They are called virtual particles. The physicist Leonard Suskind wrote in his book “The Cosmic Landscape” that the energy in the virtual photons in an area the size of your fingertip is greater than the energy all the stars that there are now in the visible universe will expend in their entire lifetime.

This doesn’t apply just to empty space,somewhere beyond the blue sky, it applies to your actual finger tip! Since atoms are 99.9999% empty space, so are you. Space filled with virtual photons. And you occupy the space of thousands of fingertips, enough for all the stars that have existed in the visible universe for 14 billion years with plenty to spare. Multiverses worth. And there is a lot of fingertips of space out there (maybe an infinite number of fingertips of space!).

What we measure is changes in energy. We follow what happens to the energy when things happen. We can measure changes in kinetic energy, the energy of movement, or changes in potential energy. Changes in movement are pretty easy to visualize, potential energy may be a bit more difficult. Changes in potential energy are due to changes in the positions of things relative to each other, say changes in electrical potential energy due to a separation of charged particles or gravitational potential due to changes in the positions of two masses relative to each other.

Energy is fundamental to all of mechanics, including quantum mechanics. Mechanics in physics relates to movement, and movement is what defines time and space. That is where the job title “mechanic” comes from: it’s someone who works with moving parts. Nothing “happens” in time and space but that there is movement of something.

Before and after, here and there.

Any event in the palpable universe, in the universe of the senses, of the relative, of conditions, of causes, of karma, of experience, of the material, of the mental, is an event because of movement (really; think about it).

Movement is the ground state of things. Everything moves. Always.

Nothing is static. Everything interacts constantly with everything else, so there is always movement. If something appears static, that is just a balancing act of opposing motions.

All things move.

If it doesn’t seem to move it is an illusion; it won’t last.