Where and When

Where and when does anything come from? Each quantum moment, each quantum space, each state of being or non being or neither, or both.

Where does it go?

Don’t gloss it over.

A thought comes from chemicals that change the electric fields of bundles of fat and protein we call nerves? How? A gift? A pattern? An emergent phenomenon? Handwaving, black box stuff.

If you use the model of a computer generating an image, that’s has a wee bit of truth I suppose from a scientific point of view or even Buddhist point of view; both have space and time quantized as a space of states, and the monitor image is quantized states of energy in each pixel. There is no continuity outside the running of a program, and each pixel is updated  individually in space and time. Movement on the screen is an illusion. Three dimensions is an illusion.

But you do know the computer has no idea there is a monitor screen let alone what is on the screen? You can program it to seem to care… but is that the same thing?

It is obvious we are in a world of illusion. No one believes there is solid stuff, right? Science talks about fields of energy. Or strings. Or forces. Or whatever. But go small enough, or for that matter large enough, and there is no thing.

So it’s all energy? What is that possibly mean? What IS it? Where does that come from, where does it go, and is it infinite or limited?

Where does the perfect, symmetric circle come from? Or the breaking of symmetry to form waves. You can’t show it to me. You can show me a cartoon of it, a sketch, an approximation, an idea of it, as I have done in previous blogs (which seems to be at times very popular, and I don’t know who or why that is), but that’s all. Doesn’t exist as a “thing” out there. But this symmetry, this perfect circle, is the basis of all scientists have to describe the world. Waves adding and subtracting, all from the perfect circle we can imagine. It is embedded in the enso and it is the Yin and Yang.

Clearly all the day-today stuff that means so very much to us, our experience of the world, all time and space, is ultimately without substance as it all arises from and merges into…. into what?

So, it’s all Mind? Sure. Easy for you to say.. do you know it or think it or believe it? Really believe it? Some say any belief is delusional. That’s Mahadyamika, emptiness, the Middle Way of Nagarjuna, Pyrrho, the early Tang Chan/Zen master’s  “ceasing of notions.”

I say that because, I don’t know.

But not knowing doesn’t stop me from trying to struggle against greed anger and ignorance. That’s practice.

Maybe sometimes not knowing even helps.

I love having a practice. Keeps me from being lazy.

But if that’s not your style, if you are reading this, please don’t forget to resist evil. I’ll be going to the march for science next week here in LA; practice isn’t really about lighting incense in robes, is it?

 

Circle Triangle Square and Symmetry redux

 

143

This is a combination of two earlier posts that seem to have been popular. I combined them and tweaked them a bit and posted it on the Hazy Moon website some months ago. This is a further tweaking, with only some minimal changes. But since those earlier posts still get a fair number of views, I thought I would make this improved version more available.

images

            It is said that “Let no one who is ignorant of geometry enter” was inscribed over the entrance to Plato’s Academy (which lasted for centuries after his death). The Pythagoreans (of Pythagorean theorem fame) made a religion of mathematics; it is rumored that they killed someone who pointed out that the square root of two was what we now call an irrational number (that is, after the decimal point the numbers never end) because the idea didn’t fit in with their model of an ordered, clean, rational mathematical universe!

Now, while the Greeks had some philosophical tendencies that overlapped with Buddhism (the skeptic founder Pyrrho went to India with Alexander the Great and studied Buddhism and the Stoics were into non-dualism and had many teachings and attitudes compatible with Buddhism), that is not why I bring up how far back the Western appreciation of mathematics reaches. I do so because it is so foundational to modern scientific thinking. Scientists consider mathematics the language of science. In fact, there are modern scientific “Platonists” like Hawking, Tegmark, and Penrose, who have written popular books and are top theoreticians in physics, who believe that we don’t need experimental evidence for their claims about reality. Rather, they believe that mathematics IS reality in its purist form! Mathematics is itself scientific evidence.

So where are they coming from and why do I think you might find it interesting if you are a Buddhist with little or no interest in Math or science? Because scientists and mathematicians argue about whether mathematics is something we invented or discovered. Because scientists are blown away by what has been called the unreasonable effectiveness of mathematics in predicting and describing scientific discoveries. Often the math was developed just for the sake of the intellectual challenge of it with no immediate practical application in mind, but then later turned out to be just the thing to use for modern science. But mostly because I see a lot of interesting overlap between what blew the minds of the Ancients both East and West and modern math and science.

Lets look at a Chinese Chan poem and then a Japanese Zen painting to see what I mean. Don’t worry if you hate math. Math is not about numbers. It is about relationships and ideals. I’ll draw you pictures.

Anything that we can experience as existing in time and space (that is, the realm of the senses) is in the realm of the “relative,” and whatever is true regardless of time and space is in the realm of the “absolute.” There is a tension between the relative, the relational, the contingent, the deep and abiding interconnectedness and interaction of what is in time and space, and the absolute. Zen practitioners know I didn’t come up with this terminology. There is an ancient Chinese Chan poem that we chant in some of our services. In Mandarin it is called Cantongqi, in Japanese Sandokai. The poem was written by Shitou Xiqian (Japanese: Sekito Kisen). Shitou lived in 8th century China. The title of the poem is apparently very difficult to translate: “The Identity of Relative and Absolute” is the version we use at the Hazy Moon Zen Center, and I like the kind of mathematical sound and unapologetic nature of  “identity.”

Books have been written and series of talks given about this poem. This poem, this relationship between the finite and infinite, the relative and absolute, change and the symmetry of changelessness, a unified force and all the various pushes and pulls that we experience in the contingencies of our lives, is one of those places where both science and Zen converge in wonder and profundity. Sages, philosophers and scientists have grappled with this throughout the ages. How do we get something from the ultimate oneness to the many things, how is there the illusion of duality if at the heart of the matter non-duality must be how it is. For certainly even scientists have some idea of non-duality. Think of the quest to unify the forces of nature. How can there be nature and something else?

The identity, or some say the harmony, of the world of the relative and the realm of the absolute is not very amenable to the intellect, to concepts and language, which evolved in the dualistic world of the senses, or even to mathematics, which gets lost in infinities. We can use some ideas from mathematics, at least as metaphors, even if just to get us started. We’ll do this by looking at the universe embodied in the circle, and to do that, lets look at symmetry and the breaking of symmetry.

There are many types of symmetry.  You can see mirror symmetry in the fluke of a whale. The right half of the fluke is the mirror image of the left, and visa versa. That is why the water is so evenly dispersed in the photograph of the fluke. Such symmetry is very functional for the diving whale. An asymmetric fluke would not work as well to stabilize the whale when she dives.

 

ry=400ry=400-2

 

 

One definition of symmetry is that you have a symmetry when something is done to a system but you can’t detect a change.

 

images (3)

If you moved this “wallpaper” over a bit to the right or left by the distance of one of the partly hidden circles, it would still look the same as long as you don’t see a tell tale edge. Pretend the square is a window with a much larger wall with the wall paper pattern on it behind the window. Move the wall, or the window, the distance of one circle to the left or right and your view through this square window is unchanged; you see the same pattern. That is a kind of translational symmetry; you translated its position without a directly detectable change; you might see other changes if you measured them, like the heat in the room from the movement and your muscles burning fuel when you shifted the pattern, or the flow of electrons in the computer if you used one and did this as a “virtual” experiment.

 The conservation laws of physics are also defined by symmetry. When we say the total energy of a system is constant, that is, that energy is “conserved,” we are saying the total energy is the same before and after you do something to the system (an experiment, say).

Look at the energy of the system before the experiment, and then close your eyes while somebody else does the experiment. When you look at the total energy of the system (including any added or subtracted, say by heating or cooling during the experiment) when you open your eyes after the experiment is done, you can’t tell there was any change in the total energy (even if the form of energy has changed, say form electrical energy to heat or the potential energy of the position of some object relative to another); it passes the “can’t tell” test that defines symmetry.

Actually we can’t measure total energy directly (the slippery nature of energy is another discussion, but even defining, let alone measuring, the total energy is clearly beyond our grasp). We can measure changes in energy. And that will be zero. If you added energy here, some was lost somewhere there. If not, you have some explaining to do. From a scientific viewpoint that can be where the real action is! A discrepancy in energy accounting could be evidence of a new particle that carried away some of the energy you couldn’t account for (this has happened), or even a new law of physics, although it is more likely you just missed something or didn’t take accurate measurements. So you try again, and if the difference remains, and it isn’t carelessness or the lack of sufficiently sensitive instruments, then you really may be on to something new! Why is energy conserved? That’s a bit far afield from this discussion, but I think it has to do with being beginningless, bottomless, endless, and uncreated.

The point is, energy is conserved and any discrepancies need to be addressed. The conservation of energy is a form of symmetry, and it is very useful.

Let’s look more closely at just what symmetry is by looking at rotational symmetry as an example. If you close your eyes and I rotate an unmarked circle, when you open your eyes and look at the circle you can’t tell that I did anything; you still see a circle, just like before. Nothing about the circle looks different. This “can’t tell” test is a hallmark of symmetry.

The entity we call a circle is an idea. It is empty of “thingness.” A circle is defined as that object that is equally distant at every point from a central point. This distance is the radius of the circle (think about it; it works!). So all it takes is a distance from a point to define a circle. We call that distance the radius. Yet in fact, no ideal circle actually exists. Even the most close to perfect circle you can create in the world of the relative is marred minimally by quantum fluctuations even of you were to design a circle to the precision of the atomic or subatomic scale.

In Japanese Zen calligraphy there are circles called enso. Of course enso are not perfect circles. They are the product of a brain, a hand, paper, ink and a brush. They are in time and space. This is the identity of relative and absolute at play, the absolutely ideal circle without beginning or end and the relative circle existing in time and space.

A perfect circle doesn’t lend itself to creating the universe of the senses, the realm of the relative. The symmetry is too good. But inherent in that circle is everything that ever was and ever could be. We just need to break the symmetry. When the rotational symmetry is broken, we can produce waves, and these waves define particles, the basis of form.

Open up a circle and you break that rotational symmetry and get a different symmetry that is limited as to rotation, but can be repeated as infinite cycles in all directions in space and time. You get the wave. We can derive that mathematically, but let me just show you a picture:

           Circle and Wave

We take a perfect circle and divide it in half. Now there is direction, duality, up and down. Now move the left tip of that lower half meets the right tip of the upper half of the circle and  we get a wave!

            You can repeat that wave (essentially rotating the circle or in this example by adding other circles in a line) without ever needing to stop (mathematically). The circle and the wave both have no beginning and no end.

The wave does have symmetry. You can flip it around the point where the two halves of the circle touch and you get the same wave (passes the can’t tell test). But it isn’t the rotational symmetry of the circle it was derived from, the unbroken circle. We broke the never ending, “absolute” rotational symmetry and found a new, more limited symmetry, the wave, which now brings us to the “relative.”

          images-4

           Mathematically we can sculpt waves. Just like additive sculpting (say in clay) or subtractive sculpting  (say in marble), we add and subtract waves to get new waves, even crafting a sharp localized spike. That spike is the particle. The really, really relative, the really, really NOT symmetric!

And hidden in a spike, that particle, there can be countless waves adding and subtracting, creating the spike mathematically.

This is Fourier mathematics, looking at the different waves that make up a given wave, and it is the basis of quantum field theory.

In the circle there is the wave, in the wave the particle, in the particle the wave, in the wave the circle.

We have the identity of the relative and absolute, asymmetry and symmetry, and the particle and wave.

SONY DSC

[The Tingari by Nanuma Napangardi, of Kintore, language Pintubi.]

 

The ancients knew about symmetry and symmetry breaking, circle and waves, the identity relative and absolute. Just look at the Yin Yang symbol! You see circle, and broken circle, wave and particle.

 

images

 They experienced it in their beings, in their lives. That is what it is really all about.

Now lets expand our look at circles and waves by looking at a Japanese Zen painting.

 

images

 

             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. After all, 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.”

 

images

 

There are many interpretations of what this painting is about.

The inscription at the left of the painting 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 and the pagoda at the temple and some nearby mountain.

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 of the triangle being the butt and crossed legs. The triangle could be meditator as mountain. The square might be the zabuton, the square pad the zafu sits on (the triangle/meditator/mountain idea was suggested in conversations with sensei Maezen at Hazy Moon).

Lets get Platonic. I would like to interpret the painting geometrically. I have no idea how much geometry Sengai knew. Clearly basic geometric shapes interested him enough to paint them.

So circles are amazing but where do squares and triangles come in? Lets start with how a square and triangle relate. A square is two triangles.

Slide2

            Next, how do circles and squares relate? Well, they could be symmetric as to area. That is, they can both have the same area despite having different shapes. That is a very useful equivalence in math and physics. Using the tools of integral calculus, which helps us deal with the areas of complex shapes, we can find “hidden” symmetries and so hidden relationships. Here is another way squares and circles can relate to each other that 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. Every square likewise defines exactly two circles, each circle intersecting with the square at four points:

Slide2

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

Slide3

          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 that defined the circle (that distance that all points were from the center point) as a minute hand, here pictured as arrows. For this illustration the minute hand will go counter-clockwise, starting at the 3 o’clock position (hey, why not?). As we rotate this minute hand radius counterclockwise we will note how high the tip of the arrow is above or below the horizontal line bisecting the circle.

Slide2

 Next lets put each vertical line (the distance of the radius above or below the horizontal bisecting line) along a new horizontal line, with each clock hour marked, starting at 3 o’clock and going counterclockwise (3 o’clock, 2 o’clock, etc.) around the circle/clock. Even with just a few straight lines we see a wave emerging if we connect the tips of the arrows:

 

Slide3

            In this figure we placed the vertical lines derived from the tip of the radius 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. More lines would get a smoother curve, a smoother wave.

 If we were to add so many arrows (each a radius of the clock/circle, that is, the distance from the center point that defined the circle) and the resulting vertical lines from the tip of the arrow to the horizontal bisecting line so that the circle is filled with lines and arrows we would get a perfectly smooth wave. In the ideal, mathematically pure case, a perfect wave, unlike the complicated messy waves of contingency we see at the beach.

What is this wave?

Each arrow is a radius of that circle. It also is the hypotenuse (the longest side) of a right triangle (and why not? Any line can be turned into a hypotenuse by adding two other lines!).

Here is one radius arrow and the horizontal line isolated (with a line connecting the tip of the arrow to the horizontal) to show that each arrow indeed defines a specific right triangle:

Slide2

This figure shows one of the triangles defined by the arrow (radius) and the line from the tip of the arrow to the horizontal bisecting line and the segment of the horizontal line that goes form the center of the circle to the line dropped form the tip of the arrow, making a unique right triangle. The circle can have as many of these triangles as you wish as the radius, the arrow, now the hypotenuse of a triangle, points to different parts of the circle.

            Now, lets say the arrow/radius/hypotenuse is one unit long. It doesn’t matter one unit of what. A unit could be one inch, one mile, one light year, one unit of 6.753 millimeters or 5.071 kilometers, or even one diameter of an oxygen molecule (although that may be subject to quantum fluctuations). It doesn’t matter a single unit of what; 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 multiples of inches, of miles, of light years, of 6.753 mm, 5.071kilometers, of diameters of oxygen molecules, etc.).

Then we can define a specific relationship between the lines of the triangle and give it a name: 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, so there no need to worry about units of measurement as any units are on the top and bottom of the ratio, so they just cancel. This ratio is just a relationship that always holds because we defined it that way. Since the arrow/hypotenuse/radius here is 1, the denominator of the ratio of the ”line across from the angle”/”arrow” relationship (the sine), so the line across from the angle IS the sine for that triangle. After all anything divided by 1 is just that thing.

Slide4

Here we see a right triangle. The thick line is the side across from the angle indicated by the curved line at the lower left. The diagonal line is the hypotenuse (the arrow, or radius, in our circle), the longest line in our triangle. To the right of the triangle we have the thick line divided by the diagonal hypotenuse (which we defined as being 1 unit long). So in this ratio, this division, the thick line divided by 1 = the thick line. The length of that thick line then is the sine of that angle (defined as the side opposite of an angle over the hypotenuse which is 1 unit)

 

We collected these sides of the triangles, which were the length of the tip of the arrow above or below the horizontal bisecting line, and we created a sine wave! So the triangle sine and the sine wave of the circle are one thing.

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 triangle, and these have relationships that define waves (we just looked at one such wave, the sine wave).

Waves have no beginning or end. We arbitrarily started and stopped at 3 o’clock on the circle. We could have kept going around and around the circle without end, and we could have started anywhere on the circle. We can go around fast, so we would have a high frequency and that would require more energy per time period. We can go around slow and that would take less energy per time period. Of course fast and slow are relative here unless you define a standard i.e. fast or slow relative to the speed of a massless particle in a vacuum, which would be the speed of light.

We could have gone in the opposite direction as well. These changes would have defined waves, just not sine waves (it would be cosine waves which are since waves out of phase, that is, shifted).

And waves, as we have seen, can add and subtract to form localized concentrations, that is, particles. Particles in this formulation are localized concentrations of the quantum field, which is the collection, or set, of potential waves based on the energy and state of a system. Wave and particle, the quantum conundrum, is then found in Sengai’s art, in the yin yang symbol.

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, even potential form that hasn’t formed? That these objects that have no physical existence but are abstractions, the product of mind, empty of substance, are the basis of all we consider substance in our quotidian lives embedded in the senses, the basis of all math and science, all time and space, the absolute inherent in the relative, the relative emerging from the absolute? Emerging in Mind?

Is this the dreams stuff is made of? Are these the parameters of the phantoms we chase?

Dogen:

“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.”

143

Photos courtesy of Susan Levinson

 

 

 

 

 

Pyrrho, Buddha, Daosim and Science

30 Kushan Buddha

In his book “Greek Buddha” Christopher I. Beckwith discusses Pyrrho, a philosopher who went along with Alexander the Great on his world tour of conquest in the late fourth century BCE.

It seems Pyrrho went native and studied with Buddhist masters. One story is that he made a lot of money as a court poet and then he was called to task by some wise guy, maybe some Buddhist sage. Was Pyrrho just singing for his dinner or was he for real? Pyrrho took the challenge! He went after ‘for real.’

When I say he studied with Buddhist teachers, I mean he practiced. His life was transformed. When he returned to his home island he lived his life as practice. He was beloved. He lived to keep it simple, keep it real.

We have later records of his teachings. He taught things (pragmata) are:

  1. Adiaphora: ‘without a self-identity.’
  2. Astathmeta: ‘not measurable’ (I would say without beginning or end), unstable (as in unbalanced, unsettling, pulling this way and that, per Beckwith)
  3. Anepikrita: unjudged, unfixed.

Those of us familiar with Buddhist terminology will see there is a connection with dharmas as what we perceive, and pragmata, though the latter may have some other, more ethical or philosophical, connotations. Beckwith compares these three with the very basic Buddhist teachings of the Three Characteristics:

1. Anatman: no (innate) Self (Identity) [Beckwith has as third but it seems more like #1 to me]

2. Dukkha: uneasy, unsatisfactory, unsteady

3. Anitya: impermanence, unfixed.

He suggests that Pyrrho’s terms are in effect a direct translation into Greek of the Buddhist terms.

Beckwith also points out that since Pyrrho was writing and studying and practicing Buddhism around 300 BCE, his form of Buddhism is probably closer to the true teachings of the Buddha than many of the even earliest written Buddhist texts. Of course it’s not like we have the original writings of Pyrrho either, we have later versions and descriptions, and the early Buddhist writings are based on a vibrant and robust oral tradition. But Beckwith does  have a point. Pyrrho’s philosophy is certainly based on very early Buddhist teachings as understood at least by some Buddhists who lived maybe a bit more than a century after the Buddha died. The fact that in what the Sutras call the ‘first sermon’ by the Buddha, as well as in many versions of Buddhism 101, the four “noble” truths (as I have done in earlier blogs) are used to introduce Buddhist thought, does not mean they were necessarily the original core teachings. It may be that is how it was later perceived or that it fit later understandings of the Buddha’s teaching (or agendas of later teachers and practitioners, as Beckwith suggests). Beckwith goes a lot further though, and you can read his book if you care about such things. If you are Buddhist, you may take exception to some of his theories. But to me, that makes it fun!

There is a great section in Beckwith’s book on the names Lao Tzu and Gautama being the same. That intrigues me. Clearly Zen/Chan is Daoism (or Taoism; pick your spelling!) meets Indian Buddhism. Not the later Daoism of gods and demons and alchemy and immortals, but the early Daoism of Chuang-Tzu and Lao-Tzu (author of the Dao De Ching). Sometimes I think Chan/Zen is as much a form of a Chuang-Tzu’s Daoism than it is a form of Indian Buddhism! Of course Chan and Zen tradition don’t quite see it that way. And the Chinese Chan masters certainly relished texts from India and the Buddhist kingdoms of the Silk Road like the Lankavatara and Diamond Sutras (they are really great stuff, read them if you haven’t and if you have any interest in Buddhism at all. Red Pine has done great translations).

Interestingly, Chuang-Tzu may have lived about the same time as Pyrrho. Of course they wouldn’t have met. Lao-Tzu lived earlier, it seems more about the time of Gautama Buddha (though dates are controversial for both)! One story in Daoist lore is that near the end of his life Lao-Tzu was said to have left China to travel west. Is Lao-Tzu and Gautama the same name as Beckwith suggests using a linguistic analysis?What does that imply? Very odd for someone who is Chinese to purposely go off to die far away in foreign lands. Very intriguing. Again, read Beckwith if you are interested in the argument.

Anyway, back to the core teachings, however they fit into the historical scheme of things. These core teachings are very scientific. Not only because they can be inductively arrived at by observation and confirmed by experience (the original meaning of the term “experiment”; same root word and that was on purpose), but in their essence.

Slide3

 

 

Regarding impermanence certainly no composite “thing” lasts forever.

Modern physics does not have a permanency of things as an essential, verifiable teaching. Not particles, not universes. Quite the opposite. There are neither fixed particles (atoms and subatomic particles are basically forms of energy) or a fixed time and space. I am not only talking about relativity theory, which does imply that time and space are not separate, fixed entities, but more basically. Much has been written and discussed on the physics and metaphysics (that is the interpretation of physics, not the study of ghosts and goblins) about time and space. We do not know the extent of time and space, or even if these things are really distinct entities, if the in fact exist other than as illusions of mind. Robert Lanza talks about this in his book Biocentrism, as do others, and I understand Dr. Lanza is writing another book about time, space and the ‘illusion of death.’

Lanza-Sangha-450

 

Regarding the lack of innate existence we have seen particles themselves are just perturbations of energy, of the ‘quantum field.’ Modern biology and the earth sciences teaches us that evolution is contingent on the environment just as the earth and its atmosphere has been shaped by life. It is the environment that determines “fitness.” Most of the minerals on earth were made possible by the oxygen released by photosynthesis and exist nowhere else in the solar system. Neither the earth or the life on it, no individual, species, or life itself for that matter is fixed and innate, a fixed separate definable entity.

And while science is about measurement, we don’t know the extent of what can be measured. Is there an eternal set of multiverses and dimensions? Were there “big bangs going back and forward forever? Again, if time and space are illusions, what could a beginning and end possibly mean?

Slide2SONY DSC

As for “unstable,” that is why there is anything at all from a scientific and mathematical point of view. I’ve written before about breaking symmetry. An ideal circle encompasses all and everything perhaps, it is certainly infinitely symmetrical by definition, but to have change there can’t be perfect symmetry. I have quoted the quantum field theory text that says that we are perturbations in a field. This is related to impermanency of ‘created things’ (is the field permanent? Is it a “created thing’?) as well. If the field were stable, there would be no things, no dharmas, no pragmata. For anything to change, to come into existence and then as it must eventually not exist, if there is to be what we experience that gives rise to the thought and perception of time and space, the system by definition must be unstable. It can’t be a system with an innate unchanging stability, a concrete thingy-ness.

There is change, evolution. There is the evolution of universes, particles, atoms, minerals, solar systems, planets, sentient beings.

As for Dukkha, unease (including but not limited to ‘suffering’ as in old translations into English), that does seem to be the nature of what happens if you yearn for the safety and reassurance of permanence, which is an illusion at best.

So science is quite compatable with anatman, dukkha and anitya.

I enjoy being challenged in my view of history by Beckwith. I enjoy seeing in the practice, writings and teachings of a poet philosopher who travelled with Alexander, a bit of confirmation that these core Buddhist/proto-scientific views were very ancient and proximate and core to the ancient teachings that underpin my practice.

Not that it really matters, I guess. Reality is reality, my practice is my practice, science is science, we live and die, however you conceive of it or dress it up or whoever may have glimpsed it before. Just kind of cool.

mob32l

 

Circle Triangle Square

 images

 

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.”

images

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.

images

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.

Slide2

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:

Slide2

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

Slide3

 

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.

 

Slide2

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:

Slide3

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:

Slide2

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?

Dogen:

“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.”

 

 SONY DSC

photo courtesy of Susan Levinson

Circle and Wave

ry=400

In my GUT of Zen there are two phrases that suggest time and space:

You are the Universe unfolding

Mind evolving.

And there are two phrases that are outside of time and space:

No beginning and no end

No separation.

Time and space are deep and difficult. Don’t be seduced by clocks and rulers and your day-to-day experience into thinking you have any idea what they are about.  The 13th century Japanese Zen master Dogen famously spilled a lot of ink writing about time and change. Change is discussed in some of the earliest Buddhist writings we have. Scientists debate the nature of time and space to this day. In a recent review in the scientific journal Nature titled “Theoretical physics: the origins of space and time” (8/23/13) there is the lament that physics is incomplete without an explanation of time and space. There are seven competing theoretical models discussed, with titles like “quantum loop gravity” and “Holography”. Continue reading