Neither Exists Or Doesn’t Exist

in all things the one, in the one all things

 

Neutrinos!

Neutrinos are subatomic particles that have just a hint of mass yet can move at light speed. They are created by radioactive decay in the sun, supernovae and some other radioactive processes like human made reactors.

Here’s the question that interests me: Do we exist in the same universe?

Neutrinos were first suggested by Wolfgang Pauli (whose exclusion principle is primarily why we can’t have two atoms in the same time and place i.e. why things seem solid when we know atoms are empty for the most part). It was known that in a kind of radioactive decay (beta decay) the momentum and spin of particles did not appear to be conserved, even though momentum and spin were known to be conserved in every other process. Hmmm. Conservation of something (like momentum and spin) in physics means that the total is unchanged before and after something happens, even if distributed differently (say one object looses momentum, but another gains it). As I wrote in earlier blogs, if you can’t tell if something changed after you messed with it, it is a symmetry. For example, if I close my eyes and you rotate a circle, it looks the same to me when I open my eyes. That’s rotational symmetry. If I close my eyes and you move it, the circle itself looks the same when I open my eyes. It is symmetric to translation.

Now, the symmetry of momentum and spin in beta decay seemed like something that better not be violated. Pauli did the math and suggested a new particle. People were a bit shook up by that, and it took 20 years to find the neutrino experimentally, but they did and it worked! This is the kind of thing that excites physicists who suggest we should trust the math: sometimes it works!

Anyway, this was part of the discovery of one of the main forces, the weak nuclear force, which has been unified with the electromagnetic force (the electroweak force) and so is a big deal.

Neutrinos have no charge, but like the electrons they are related to (which have charge) they have spin. Spin is weird. Point particles can’t literally spin around (there is no axis or lateral extent to spin around the axis; they’re points!), but the term spin is used because the particles behave like spinning particles would (like how they move in magnetic fields). Well, something is weird with neutrinos; they have a preference and they shouldn’t! Neutrinos are “left handed” and anti-neutrinos “right handed” (the direction of spin) and that is weird. Unlike the other situations mentioned above, we can’t just flip the terms and it is just how we say it, it doesn’t matter which you call which. It isn’t symmetric. It may not seem it, but that is really unique!

Yikes!

There’s more.

When they measured how many neutrinos/second came from the sun, it was less than expected. It turns out there are 3 flavors of neutrino that can change into each other. They “oscillate.” Other particles don’t do this, at least not in the same way. It was once thought that maybe all three types (flavors) of neutrinos don’t have mass. That was wrong. They have mass. But we don’t know the masses of the three neutrino flavors; we only know the differences in the mass between them. Anyway, neutrinos interact differently with the Higgs field (which gives mass) compared to other particles. So it seems all three have some really tiny mass, way below other particles with mass, but tiny as the mass is, they are not massless like photos and gluons.

I have seen various estimates for how many neutrinos pass through you, but it is something like 100 trillion per second, every second you are alive.

Why don’t we have any effect from them? You don’t hear about putting neutrino sun block on. In fact, if you could see neutrinos, it is said the sun would be as bright as the full moon. That is neutrinos from the sun wouldn’t be as “bright” as photons (regular light), but it would be plenty.

It’s because they interact very weakly with matter. We are invisible to them and they are invisible to us.

How weak is this neutrino interaction with stuff? According to one estimate, neutrinos interact with atoms so weakly that it would take about four lifetimes for one to interact with an atom in your body despite the trillion going through every second. Askel Hallin in Scientific America wrote that in the Sudbury Neutrino Observatory, a 1000 ton heavy water solar-neutrino detector picks up about 1012 (1 with 12 zeros after it i.e. a trillion) neutrinos each second. About 30 neutrinos per day are detected, say about one per hour). There are 3600 seconds in an hour, so about it seems that almost 3,600 trillion are “picked up” in the detector (his word, I believe that means passes through) for every one neutrino detected (that is, that interacted sufficiently with their apparatus to be detected).

The universe of the neutrinos is: be created, have a tiny bit of mass, and exist in a vast empty universe. Most will go light years without interacting with anything, cruising through planets, dust clouds, people, whatever.

If neutrinos could somehow put together all the vast neutrino “data” of the rare and random neutrino/matter (subatomic) interactions throughout space and time, some objects would have enduring patterns and become “visible”, or perceived in the sense of registering interaction/o interaction, yes/no, 0/1 information. That is, an interaction event happened that changed the information content of the universe that could be considered a “perception.” If enough events/perceptions were gathered over time, there would be entities that would be denser to neutrons than their surroundings and persist long enough to be present in the neutrino universe. Perhaps stars and planets and nebulae would be large and persistent enough to exist in the neutrino universe.

But neutrinos wont ever “perceive” you or me. The neutrino world of can’t resolve us as anything but a single data point that would be lost in the noise of other random and rare interactions, if we as individuals have such an interaction at all. Remember that most of us (3 of 4) wont ever interact with neutrino world; we are truly invisible. If there are four of us, yeah one of us was “seen” but at such low resolution (a single 0/1 for all space and time, just one data point, one interaction with one neutrino and one atom) that in neutrino universe he or she would be no different from a falling leaf, the air or water in a mountain stream or a wandering cosmic particle in empty space. Just a bit of noise, if even that.

As a small practical issue, if some genius advanced aliens did have neutrino vision, the neutrino data, the “perceived” patterns that persist through a sufficient time at neutrino interaction scale (many, many, many human lifetimes) on a planetary level that could resolve say our planet, would require supercomputers to even approach giving any real image. After all, our planet is a moving target; around the sun, then around the galaxy with the sun, then the galaxy rotates and moves and space expands. Just looking at an area in space would be useless. Any object would be gone.

We are invisible to neutrinos; we simply do not exist.

Are neutrinos invisible to us? Well, they were until a few decades ago. Certainly they are without huge and expensive detectors. They pass through us (and our planet) with impunity, the rare interactions too weak and isolated to have any abiding effect on any macroscopic entity. They are without direct effect and certainly in that sense non-existent.

Now, here is a neutrino universe we have discovered and added to (with nuclear reactors), the neutrino universe of radioactive processes, the sun, supernovae, our reactors on earth, that through science we can “perceive”, but barely, that interacts so rarely that we as individuals can never exist in that neutrino universe.

And despite having mass a neutrino travels at the speed of light (some scientists thought they saw evidence of faster than the speed of light neutrinos, but so far doesn’t seem true. Information in entangled particles can transcend time and space, for example, but it doesn’t seem neutrinos can). As I have written elsewhere, travelling at the speed of light means the ultimate n space contraction (there is no here to there, only start then place of interaction, no here to there) and time dilation (the next tick of the clock never comes, just start and time of interaction, no then to now.)

A neutrino universe is our universe, but then again, it isn’t.

All of this about neutrino world as written sounds a bit like pantheism or maybe just bad “anthropormorphizing” if you take it that I mean literally that the neutrinos are self aware and communicate these interactions. But in math and science you can talk about a space of states. Here what I mean is the space of neutrino states as encoded in 0-1, neutrino yes/no, interaction/interaction with a subatomic particle, exists independent of our experienced universe.

And here is my point:

In that neutrino space of states I do not exist. Literally. I do not, I cannot, exist. I am in a space of states  (e.g. momentum and energy) that interacts too rarely with neutrinos to register as more than noise, if it registered at all. The sum of neutrino universe interactions would not be sensitive or specific enough to detect that I exist.

Neutrinos do not exist for you and me, even if we look them up on Wikipedia. You may trust me as I trust the physicists, but there is no consequence to you of the vast number of neutrinos that pass through you undetected that they truly do not exist for you except as a rumor that you have. If you aren’t a physicist or part of a team researching neutrinos, they don’t exist but as a story.

Really, they just don’t exist.

But…they do exist, these children of the stars.

And whatever space of states neutrino world evolves through, you don’t exist.

But…you do exist, a set of various spaces of states, whether or not it “matters” to neutrino world.

In Buddhist sutras there is a category of what neither exists nor does not exist. Not Aristotelian, trying for non-dual logic.

Neutrinos: You bet.

 

 

 

 

 

 

 

 

 

 

A Graphic Book Conversation About Physics

If you are interested in taking a peek into what a theoretical physicist who seems to be more interested in being honest than making a splash (or name for himself as an arrogant hard core crusader) would like you to know about his views on fundamental physics and metaphysics try “The Dialogues; Conversations about the Nature of the Universe” by Clifford V. Johnson. He’s at USC  but I forgive him (UCLA joke). I use the word metaphysics in the sense of the interpretation of physics, not spiritualism or the like. It is a graphic book (novel? Kind of? In his preface Clifford seems fine with comic or any terminology). The art is good, some panels even more than needed (a lot of work went into this!), but the reason I am highlighting the book isn’t the graphic art, as much as I appreciate it. I enjoyed the frank, honest talk about the limits and joys of science, particularly math and physics.

It is hard to convey that feeling. I’m not a physicist, but I “do” medical science research, and I know the feeling of discovery and wonder. I have tried to give a taste of that in some of my earlier blogs. I may have been partially successful; my “circle triangle square” blog gets the most hits of any I have written. I spiffed it up and re-posted last year ago or so but I think it is still the original that gets looked at. The hits sometimes come in bursts so I wonder if someone uses it for a class or discussion group. You’ll have to judge for yourself whether Clifford does it for you, but I think he makes a good effort. I recognized much of what I love about basic science and math in his graphic book.

Consider spending a couple of hours with this book. That’s all it takes to read it. You’ll learn some physics and how at least one theoretical physicist thinks about what he does as a theoretical physicist.

Spoiler alert: regarding physics: it ain’t over, and for that matter the fat lady may never sing. Physics is a process with no definitive end in sight. Theories of everything are a dicey proposition and at best may be untestable conceptual frameworks with a series of equations empirically describing what we can measure regarding energy flows. It’s a jigsaw puzzle with no picture on the box (a metaphor he uses) and all the pieces may not be able to be grasped or measured by our finite brains and resources.

We knew that, didn’t we? Still, if you like the scientific conversation, read Clifford’s book.

If, on the other hand, you want to know more about science and implications of consciousness on the nature of reality, stick with the books on Biocentrism by Lanza and Berman for a more quantum based approach or Bernardo Kastrup’s works for a more philosophical approach. I haven’t run into anything new on that front. I suspect that’s not a coincidence. Those authors do a great job, physics is physics some new interesting stuff but so what, and Zen is Zen.

And samsara is samsara. Arrrrrgh. Keep the faith, don’t let them get you down as they hurt and destroy to feed their beast, their greed and anger and ignorance. Do whatever you can to do good and to stay strong.

My love and hopes for a better world to all.

 

Circle Triangle Square and Symmetry redux

 

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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.

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            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.

 

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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.”

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           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.

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[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.

 

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 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.

 

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             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.”

 

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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.

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            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.”

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Photos courtesy of Susan Levinson

 

 

 

 

 

Two Sutras, a Poem, the Brain and Everything

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I like that Buddhism says that mind, as in brain process, not Mind as in Buddha-Mind, is a sense perception, that the brain is a sense organ, like the eye and ear in seeing and hearing.

The brain is indeed a sense organ in that it evolved to organize energy inputs and channel them to other parts of the brain, just like sense organs do. Only the brain’s output is a context, that is, a story. It is a “meta” sense organ in that it organizes the other senses. And just like the eye can generate it’s own output without “external” inputs (close your eyes and you will see things, colors and lights, generated by random firing of retinal cells) the brain can generate it’s own outputs without inputs; we call them thoughts.

In fact, some would say this is the nature of all of our experience of the dualistic world. We project the universe we experience our brain processes, like the Lankavatara Sutra says.

Too abstract? Try this. Each eye sees only 2 dimensionally. It has to; the retina is a flat sheet in the back of your eye. We project a 3 dimensional world. Our brain compares inputs from both eyes to make that story up. We can do it with one eye, even though there can be no 3 dimensional perception with just one eye. We do it by what we have been conditioned to expect, based on evaluating relative size, shadows, etc. That’s why pictures can look 3 dimensional to us, whether paintings, movies, photographs, TV, etc. It’s why optical illusions work and why one-eyed people don’t walk into walls (at least not a lot more than two-eyed people) and can drive.

How about this? You can’t see a “yellow” photon (that is, a photon at the energy we describe as yellow as shorthand). You have no yellow perceiving photoreceptors. Your brain puts yellow together from various inputs from the retina and projects it back out

Those inputs from one part of the brain (the visual cortex) to other parts of the brain (the visual association centers that put together the world into a coherent visual story) are no different on a brain level than the input of a photon on the retina of the eye that causes changes of energy that are then transmitted to the brain in the first place. Energy in, energy out.

So yes, the brain is indeed a sense organ. Well done, ancient Buddhists!

Lets go wide and deep on this.

first, go small, very deep, to strings, if they exist, we get to just energy patterns. At that level, there are no things, things disappear.

Go wide and big and in the vastness any thing, any fluctuation in the energy, you, the galaxy whatever, even our universe, is so negligible as to be essentially if not actually zero. Like a tiny + and – adding to zero. All change in the realm of what we (our scale of energy fluctuation) can perceive even extended by instruments, is no change at that scale, in the face of infinity, or 10^500 multiverses, or even in our known visible universe, or especially, as I understand it, if there is indeed no beginning no end. At that level, there are no things, things disappear.

So we are back to Shitou and the Tang dynasty Zen poem “The identity of Relative and Absolute” wondering what this vast UNI-verse, this undivided non-dualistic state, and awareness. What is that identity? How do we get to the reductionist stuff from the unified forces or to the unified forces form reductionist stuff? That is true science, the real theory of everything; only it isn’t a theory.

This brings to mind The Diamond Sutra, which says we should not attach to a person, a soul, a defined entity and identity of who and what we are.

To the state of being at the smallest of the small, say a “string” or the smallest quantum fluctuation of virtual particles in the void, at the smallest scale, you don’t exist. That is why a virtual particle, an expression of the vast limitless energy of the void, is “virtual;” it doesn’t feel us and we don’t feel it. Otherwise it would be a particle, not “virtual.” Yet some say that energy is where the big bang, or all existence, came from. It is fundamental. It is “the field.” Others say fields are just concepts that tell us how things act, to do the math (that is, quantum fields can be described by how they work, not what they are). In any case, there is nothing you can do to touch that string or virtual particle, you are too large, too coarse. That smallest world exists in a cosmos that isn’t yours, yet it is you. Yet you only exist as an individual entity (to the degree that you seem to do so) by virtue of the rules of the smallest of the small.

To the Universe/cosmos or multiverse or whatever, at the largest scale you don’t exist. You are too small a blip to register in the unending beginninglessness. Heck, even at the level of the galaxy, our solar system is too small to truly be said to exist as more than a small statistical fluctuation. At larger levels we aren’t even statistically present. Yet you only exist as an individual entity (to the degree that you seem to do so) by virtue of the rules of the biggest of the big.

And in fact, science tells us that there is no privileged time and space, that every point is the center of the universe

That cosmos, the smaller and smaller, or the bigger and bigger, that we can’t seem to touch, is us, because, well, here we are, right dab in the middle of it all.

The ancients would ask a new student “where did you come from?”

Meaning where are you? When are you? Who, what are you?

Good questions. And in some way, science and Buddhism start to converge in the answer.

You are the universe unfolding, without beginning or end, neither here nor there, neither existing or not existing, at least not in the way you think with your sense organs, your day to day relative existence, yet always at the center.

Please, lets take good care of that center!

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