Viral Brains

In my last post Charles Darwin and I put us on a footing with worms as sentient beings with intelligence. And I encouraged feelings of deep love for mud. But lets note our very very intimate relationship with and debt to entities that are not even quite living by any definition: viruses.  Part of our genome, our collection of genes, including DNA that doesn’t code for proteins and used to be considered “junk” but is now known to include critically important stretches of DNA that determine which genes will be expressed (that regulate the genes), is actually derived from viruses. Such viruses result in DNA that has been incorporated into our genome, and it turns out that we may in part owe our mammalian intelligence to these viruses!

And going the other way to now extinct cousins, if your ancestors left Africa before some 50,000 to 75,000 years ago then  1-2% of your genes are variations from your ancestors having sex with Neanderthals and 30-80% of the Neanderthal genome are variants can be found to be in the modern human genome, shared by those of us early out of Africa types.

Why do I bring this up? To remind us that what we are is the same thing as viruses and Neanderthals. Or if you are a later out-of-African, not Neanderthal, but still viruses!

And sure, we share genes with bacteria, and plants. And we are made of elements brewed in stars actually, we are like complex planets. But that sounds more acceptable somehow, I think, for most of us. Sure we are star stuff, sounds awesome, but viruses, and Neanderthals?

When the old masters said “Buddha is shit” or Buddha is a worm” or “Buddha is a virus or Neanderthal” or “we are mud” (ok, they probably didn’t say that) they weren’t speaking in riddles, metaphors or trying to shock. They were simply being accurate.

Year of Mud and Worm Intelligence

There is a wonderful editorial in the scientific journal Nature this week entitled “Down to earth” (Nature News and Comment, Nature volume 517 issue 7535, Jan 20, 2015) about dirt, about mud about soil. The Food and Agriculture Organization of the United Nations (FAO) has declared this the International Year of Soils.

Soil, dirt, IS life, at least here on earth.

What is the difference between dirt and soil as positive or negative words? Just where it is relative to where we WANT it to be. When a baby “soils” her diapers, it is because we don’t LIKE to deal with shit that we use the word soil. We wish it would just be somewhere else. When we track dirt into the house, it is dirt, not soil, because we wont use it to grow stuff. Well, those of us who lived for a time with dirt floors know that is kind of arbitrary. It is about aversion and attraction based on… what to you think?

But soil, dirt is life, as basic to our embodied existence here on this planet as the sun and water. And bees. And the only thing of that bunch we are not messing up is the sun; that we are merely wasting but not using more solar energy.

Which brings me to Charles Darwin and worms. One of the first scientists to really appreciate the role of living organisms in shaping the earth, and not just the other way around, his last book written in 1882 was “Vegetable Mould and Earthworms.” Yes, he not only was at the forefront as I have detailed before in animal minds and emotions, but he was also a visionary in ecology and the very thin (one might say essentially non-existent) veil between our earth and life.

Vegetable mould is the part of the soil that is composed of organic matter derived from, or processed by, living organisms. And worms play a central role. As I mentioned in a previous post, one of the world’s longest experiments is the settling of a round stone in Charles Darwin’s backyard as earthworms eat the soil form under it and shit it out elsewhere. He even documented this process at Stonehenge!

Darwin worm stone

Darwin’s worm experiment


Effect of earthworms on stones at Stonehenge from the book Vegetable Mould and Earthworms (1888 edition)

But while recognizing the ecologic value of worms and dirt is all well and good, here’s a challenge I suspect most of you will be able to rise to: do you think Charles Darwin thought earthworms are intelligent? Or do you put him in a box of “scientist” who can’t possibly see that they could be sentient beings, who sees all life forms as mechanical automatons.

Well, you know from how I asked it (you did go to school, right?) what the answer is. I quote:

“Judging by their eagerness for certain kinds of food, they must enjoy the pleasure of eating. Their sexual passion is strong enough to overcome for a tie their dread of light. They perhaps have a trace of social feeling, for they are not disturbed by crawling over each other’s bodies, and they sometime lie in contact… they pass the winter either singly or rolled p with others into a ball at the bottom of their burrows Although worms are so remarkably deficient in the several sense-organs, this does not proceed intelligence… we have seen that when their attention is engaged they neglect impressions to which they otherwise attended and attention indicates the presence of a mind of some kind. [comment: some level of free will as Thomas Campbell might suggest?] They are also much more easily excited at certain times than others.” [p 35]

Later in the book Darwin has 32 pages in chapter 2 on “Their Intelligence” where, as a good 19th century naturalist, he collected data on how worms chose what material they used to plug their burrows.

So while many scientists might indeed question whether worms are sentient, WE (you, me and Darwin) won’t, will we? Like Darwin, we recognize sentience when we see it, don’t we? And we are certainly big fans of dirt and worms. Our lives depend on it!



Belief Traps


The Diamond Sutra professes that we mistakenly believe in ourselves as persons that are persistent and real entities. We make it up. We want to believe we are this and that and more.

The Lankavatara sutra discusses how we approach reality blinded by  our perceptions and projections, creating rabbits with horns.

A Zen Master said, name the color, classifying it and believing thereby that you know what it “is” in some concrete and enduring manner, and you blind the eye.

As the Enlightenment polymath and genius Laplace is supposed to have said on his death bed, we chase phantoms.


We want to grasp intellectually, to touch, smell, taste, see, and hear it all. And when we can’t, we fill in the blanks with what we believe should be there, projecting our beliefs, like the way our brains fill in the physiologic/anatomic blind spots in our vision or the details in our peripheral vision that we don’t really see.

We are trapped by our beliefs, and they don’t have to be the clearly wrongheaded absurd beliefs those other people believe that lead to such disasters all of the time, as we can plainly see. Seemingly benign and elegant beliefs can still trap us and become a filter, a distortion, an unconscious bias that keeps us in a fog of delusion, keeping us in a stupor of ignorance.

On top of that, when we have sufficient insight to discover a belief we might be trapped by, a cobbled together way to pretend to ourselves that we know what we are talking about, to explain ourselves and to make our selves more comfortable, allowing us to at least have the illusion that we have some control over things we don’t really understand or have the big picture for, we often simply replace that exposed belief with a more subtle or palatable belief.

We use beliefs as shortcuts, to make our lives easier. That may be a necessary temporizing measure, but it doesn’t work for long. Our beliefs often confer a false security. We are like the turkey that thinks seeing the farmer means feeding time, until of course he is carrying an axe one morning in late November.

This is because beliefs, to the extent that they are beliefs, reflect our state of ignorance, which means our degree of entropy and disorganization, the energy not available for us to use consciously and conscientiously (more on entropy, ignorance and information later), and are at best simply a set of working hypotheses to guide us until we evolve and mature in our actual experience of reality.

Both Buddhism and science (though not all Buddhists or scientists, of course) stress experience (the word “experiment” was derived from the word “experience”), not authority or beliefs. But lacking the requisite experience and maturity, driven by fear and grasping for reassurance, we can’t abide empty files, incomplete knowledge or unclassified experience. They taunt us and remind us of our ignorance, our tentative situation. Of impermanence. Of our limitations in the world of the senses.


Of course, that is in part why I have thought quantum mechanics might be worth looking at at all for a student of Zen. Whatever interpretation of what quantum mechanics is “really” about that you favor, quantum phenomenon minimally demonstrate that we have to resist trying to jam reality, even experimental reality, into the “how it really is” mentality of the beliefs we hold, the classifications we walk around with in our heads based on our day-to-day experience in the 4-d world of the senses at the level we experience energy transformations.

It won’t fit.

You can jam your experiences into your beliefs and your beliefs into reality, then close the lid, like pushing a spring loaded clown into a Jack in the Box, but eventually the music will stop and pop goes the weasel.

This includes beliefs in materialism (science), Platonism (math), philosophy, post-modernist relativity, religion, political or social ideals, or artistic/poetic ideals like beauty or romantic love, and yes, even Buddhism! To the extent that they are indeed beliefs that are treated as more than mere provisional models to orient you (or say Buddhism as template, as Nyogen likes to say), to the extent that they are concepts, files you need to fit your experiences into, rigid structures that can not expand as you grow and evolve, I suspect that they will sometime or another fail. And then they will cause pain and suffering for yourself and others. Or at least disappointment and disorientation!

I bring this up today because I came across this sentence that I wanted to share in a book called “My Big TOE” by Thomas Campbell:

“Jeez those belief traps are amazing – they can transmute simple ignorance and incompetence into blind stupidity in a flash.”

Been there, done that!

Beliefs: a very, very subtle practice.


photos courtesy of Susan Levinson

Indra’s Web and Quantum Entanglement: What Happens Here Happens in Everywhere and Everytime


Quantum entanglement is a phenomenon that, like the two slit and interferometer experiments we looked at previously, makes a mockery of our day-to-day experience of time and space. It brings to mind the vast and unyielding interconnectedness that is Indra’s web.

Let’s say we generate two particles at the same source at the same time from the same material and send them in separate directions. These particles are entangled. What does that mean? It means what I do to one has an immediate effect on the other. They are one system throughout time and space.

Suppose I measure some property of one of the particles of a pair of entangled particles. We can measure the polarization of a photon. Polarization is the orientation of the electromagnetic field of a photon (or en masse of a beam of light). Polarizing filters in glasses block horizontally oriented (polarized) photons that might be reflected off the road or a lake surface, for example, to diminish glare. Both photons in an entangled pair will have the same polarization when measured. Measure the orientation of the polarization of one photon of an entangled pair (say you find it is either horizontal or vertical), when you measure the other photon in the pair it will be in the same orientation.

Or we can measure the spin of an electron or similar subatomic particles. Spin is not really quite spin like say a top or dreidel, as point particles don’t have dimensions like width to be spinning. But certain particles like electrons do have a kind of axis with a direction that can be determined by their interactions with magnetic fields. This spin has momentum of spin, and this angular momentum is conserved, as momentum is energy and energy is conserved; this is an important symmetry. So if one electron of an entangled pair is spin up, the other will be spin down when measured.

Now the most important phrase is “when measured.” This is critical because one of the aspects of entanglement that makes it so mind blowing is that it simply cannot be said what the polarization of either photon or the spin of either electron in the entangled pairs is until a measurement is made. Just like we saw before: there is no what it “really” is. There is no which of the two slits the particle “really” takes or which of the paths in the arms of the interferometer the particle is “really” in. There is superposition. Similarly, there is no spin or polarization until it is measured in one of the particles of the entangled pair. It neither is or isn’t! Such a dualistic, concrete material notion of what is or isn’t doesn’t work!

That should come as a surprise. After all, if I have a pair of shoes, with one shoe here in the room with me and the other shoe in in another room, and the shoe here is a left shoe, the other is going to be a right shoe (much like spin). If one shoe is black, the other will be black, if one is white, you can bet the other is white (like polarization). No great mystery. These are the properties of the shoes! So why can’t it be the same for entangled particles? The properties are inherent, even if sometimes hidden. Surely the property is there, the is or isn’t of it exists, we just don’t know what it is.

But no, there are no hidden properties. There really is no sense in which the particle has that property until it interacts in some way that demands that property, until that is, it is measured. A physicist named Bell suggested a mathematical way to test this and the experiments were later done showing to the satisfaction of almost all physicists that there are no hidden variables in these entangled quantum particles (though, as in so many aspects at the edge of physics there are some who dispute whether the final word is in). The logic for this “Bell’s inequality” is a bit complex so rather than get distracted now I will save it for another post for those interested (a book I recommend if you are interested in that by a world class quantum experimentalist that is written for lay readers and goes into this is “Dance of the Photons” by Anton Zeilinger. Zeilinger is the one who did the experiments showing Bucky balls of 60 carbon atoms have a wave function that will show quantum interference).

One reason I don’t want to get into Bell’s logic now is that there’s more to entanglement and I don’t want to get distracted but the math.

There is nonlocality, spooky action at a distance, as Einstein put it. It doesn’t matter how far away the two entangled particles are when one is measured. Scientists are convinced you could be a million light years away from the scientist measuring the other particle, trillions and trillions of miles and the million years it would take a photon to get from one scientist to the other would collapse into no space and no time separation the instant you measured one of the particles. Information, according to the theory of relativity (say about the spin of a particle), is not supposed to travel faster than the speed of light, but the measurement of one particle of a pair of entangled particles determines the properties of both particles immediately, whether the particles are a tiny fraction of a millimeter apart or they are so far apart that it would take light a million years for information as we understand it and normally experience it to traverse the distance separating them.

Clearly it isn’t a question of sending information across time and space!

And there is more. For that, lets get back to Anton Zeilinger.

Anton Zeilinger, the experimental physicist from Austria, whose book I mentioned above, is an interesting guy. He met with the Dalai Lama and other researchers and Buddhists in one of the Dalai Lama’s science and Buddhism meetings, and his talk is reported in “The New Physics and Cosmology: Dialogues with the Dalai Lama” Edited by Arthur Zajonc, 2004 Oxford University Press.

Zeilinger starts by noting: “in classical physics and everyday life a mountain is there even when I don’t look. In quantum physics, this position no longer works.” Later the Dalai Lama asks him if “nothing can be said about the nature of light independent of the measurement whatsoever?” Zeilinger responds “that’s right.” As we have come to several times thinking about quantum experiments, it is neither there nor not there. It neither is nor isn’t, until it is or isn’t in experience.

Zeilinger goes on to discuss the double slit experiment we have gone over before. When the Dalai Lama asks if particles interact like billiard balls demanding physical contact, Zeilinger makes it very clear that “in quantum physics we have given up such pictures” and “we should not have pictures anymore” as “all pictures fail”. We are misled when we extrapolate our day-to-day experience into this realm, one of the real lessons for Zen students and the rest of us in quantum mechanics. Even science asks that you give up your prejudices, your conditioned perceptual expectations!

He says that all of this “holds not only for small things” [e.g. photons and electrons and Bucky balls] “but also for large things. It’s not a question of size; it’s a question of economy because the larger the things become, the more expensive the experiments get.” It is true that ”physicists now believe that the world is quantum mechanical through and through.”

In discussing entanglement he brings up nonlocality, which is at the heart of what we have seen so far. After all, what I do in Vegas to a photon should stay in Vegas, stay local, unless there is a local to other local to other local transmission of information. A signal propagating through space and time, a photon flying through space from a star to our eyes at the speed of light, or a signal somewhat less quickly moving through a fiber optic cable. Continuous movement, no interruption, here to there, to there, and then to there, through space and time in a predictable and well behaved manner that can be timed and followed. But as we saw, that isn’t what happens in entanglement!

As Zeilinger says “under certain circumstances two particles remain one system even if they are separated by a very large distance. They are not really separated in a deep sense… We can keep going and talk about four or five or six particles. It never ends.”

The Dalai Lama then asks: “Are you implying that the entire universe is internally entangled?”

“Anton Zeilinger: That’s a nice idea, but I would not want to take a position on that because, as an experimentalist, I would not know how to prove it.”

OK, for now we can give him that. He’s trying to be honest and stick to what he knows. It’s his job, he feels responsible to the rules of his physics discipline and to his physics brethren and he won’t speculate. We all should do that to some degree, keep to what we know, though I clearly don’t always; that would not be nearly as much fun. In any case it was pretty cool for him to put himself out there as a physicist and be open. As you can tell, I enjoyed their discussion that also goes on to randomness and causality, but enough for now.

Anton Zeilinger has done very far out entanglement delayed choice experiments. Let’s look at one. If Alice and Bob (they always show up in these things; it is really standard nomenclature in information theory and cryptography to invoke Alice and Bob) each create a pair of entangled particles and send one from each pair to Victor so he now has a pair of particles, one from Alice and one from Bob, and then Victor entangles this pair, then Alice and Bob’s remaining particles will also be found to be entangled, even though they didn’t interact directly! This is called entanglement swapping. If Victor doesn’t entangle his pair of particles, then Alice and Bob’s particles will not be entangled. So you can find out what Victor did by seeing if Alice and Bob’s particles are entangled.

Very clever!

But what if Victor makes his choice AFTER Alice and Bob make the measurements that determine whether their particles are entangled, even if only a tiny time bit after?

You guessed it; what Victor decides and what he does with his particles, even AFTER Alice and Bob measured their particles, will determine what they will have found, whether or not their particles are entangled.

Zeilinger and his colleagues published an article in Nature Physics describing such an experiment (Xiao-sung Ma et al Experimental delayed-choice entanglement swapping, published online 4/12): “This can also be viewed as ‘quantum steering into the past’.”

They end their article saying: “Bohr [a famous founder of quantum mechanics] said that no elementary phenomenon is a phenomenon until it is a registered phenomenon. We would like to extend this by saying that some registered phenomenon do not have meaning unless they are put in relationship with other registered phenomena.”

Like Anton Zeilinger suggests, maybe we should have no pictures, and indulge no speculation beyond the data.

It is enough perhaps to realize that you can’t depend on such pictures, concepts derived from your day-today life at the scale at which you experience the universe with your senses.

But Indra’s web, vast and interconnected beyond imagination, really is a great non-picture picture!



All Buddhas Throughout Space and Time (and you and me and everything else)

This is how Lancaster and Blundell begin their book “Quantum Field Theory for the Gifted Amateur” ( note: by “gifted amateur” they mean someone who knows something of the math of basic quantum mechanics, relativity theory and Fourier transforms, but is not a professional physicist!):

“Every particle and every wave in the Universe is simply an excitation of a quantum field that is defined over all space and time.”

I remember the first time I heard in our service at the Zen center the part of a chant that goes: “all Buddhas throughout space and time…”

Pretty straightforward, and I suppose not exactly quantum field theory, but I was hooked.


Quantum Peak: Where Are You? Where Are you Going? Are you Sure?


Hakuin Zenji occupying the ground he sits on. Where is he?

Heisenberg’s Uncertainty Principle!

Most of us are uncertain about this or that. In quantum mechanics uncertainty isn’t a matter of confidence or knowledge, it is in the nature of the beast.

I am often amazed how this uncertainty principle is seen by scientists as such a strong principle that observations and outcomes must obey it. No questions asked, no reservations.

Here’s what it says:

There are measurements, things you can know about a particle, say a photon or electron. Some of these come in pairs such that both cannot be known to the same degree of certainty at the same time. Period. Our ability to measure the universe with our senses (and our devices which are extensions of our senses), what we can know by observation, is fundamentally limited.

Often it is said that this is due to the clumsiness and coarseness of our measuring devices. Send in a photon to “see” where the electron is by pinging it, and you now have an interaction that changes things. The size and energy of what you use to “touch” the world of particles is so large proportional to the particles, you can’t help but disturb it, to change it as you measure it.

Fair enough.

But it in fact goes more deep than that.

Lets look at momentum and position.

Momentum is how much oomph something has when it is moving, how much bang it would have if it hit something. If the object has mass, momentum is simply mass times velocity. The more massive the object and faster it is going in a specific direction (velocity is speed and direction, a very important point), the more momentum it has. Since photons have no mass, the momentum is a function of its energy, or wavelength, but that matters little to us here. The idea is the same, directed energy, how much oomph it has in a specific direction.

Lets look at an experiment, shining light at holes in the screen. The light is represented by the golden arrows going left to right.


If we shine a wide beam of light with many photons against a screen that has a hole in it, most of the light is spread out pretty evenly along the screen and will hit the screen pretty evenly all over (well, an area of the screen as large as the beam is). We don’t know where in that beam a given photon is exactly. It is in the room between the light source and the screen it was aimed at, but a given photon can be positioned anywhere in the beam of light (the straight arrows to the left of the screens in the illustration).

But assuming we know the wavelength of the light, and the direction the beam was pointed, we know the momentum of any photon in that beam with a great deal of accuracy. The beam was directed toward the screen, and so if undisturbed should be going pretty straight on (except for the stray cosmic ray or atom in the air hitting the beam, for example, pretty small effects here and they can be minimized), and at the speed of light in air, and so we pretty much know speed and direction pf the beam and so all the photons in it. So while the momentum of individual photons will vary a bit, it won’t be by much.

We can say then that before the light gets to the screen we have little (but some) information about position of the photons in the light, but a lot of information about momentum of the photons.

Next, some of the light goes through the hole on the screen at the left in our illustration. There is a phenomenon called diffraction. When the light leaves the hole, it bends out at the edges. The larger the hole, the less relative bending, the smaller the hole the more bending. Picture a broad water wave going through a small opening in a jetty. On the other side of the hole in the jetty the wave will expand. If it is a big hole, most of the water wave just goes right through undisturbed, only the part of the wave right at the edge of the opening in the jetty is going to spread out again after passing through. So big opening less relative rate of spreading.


A broad wave on the left goes through the holes and then spreads out. This is another way to see diffraction. In this case there are two holes and so the diffracting waves interfere. We will limit ourselves to one hole this post!


Our light now goes through the hole in the screen on the left below.


Only about two arrows from the light on the left enter the hole. We know where the hole is, so now we have a lot more information about position of photons just after they enter and and right after they exit the hole than we had before the light entered the hole. We know pretty well where that light (and any given individual photon in the light beam) in the hole is when it is in the hole or just after it exits the hole so we know with a high probability where a photon that is going through the hole or just exited will be found, much more so than before the light entered the hole.

But due to diffraction induced by the hole when the light exits the hole (to the right in the illustration) the beam spreads out. But at that point, at the exit of the hole, that tails of the arrows are close together, and the area the photons can likely be found is about the size of the hole, so we still have information about position that is much more precise than before. An important point is that it right after the hole at the base of the arrow that matters. It is the direction of the arrow, not what is happening at the tip that counts here. What we see though is that only the central arrows of light are still going in the same direction that they were before entering the hole, as they were not affected by the edges of the hole (really mostly the most central arrow) and are not diffracted. So while we know we will find a given photon in the area about the size of the hole, if it was at the edge of the beam its direction (hence momentum) will have changed considerably. So some photons have the same momentum, but many have changed. We are less certain about momentum because remember, momentum isn’t just speed (the speed of light didn’t change) but also direction (and that for many photons that has changed due to diffraction at the edge of the hole).

We went from knowing little about the position, and a lot about the momentum, to knowing a lot about the position and much less about the momentum of a given photon. The possibilities for position have decreased, the possibilities for the momentum have increased.


On the illustration above, we made the hole in the screen on the right smaller. Now only one arrow from the light coming in from the left  gets through. You guessed it, we then have more information about position on the other side of the hole. It is confined to a smaller area due to the smaller hole. But since the hole is smaller, on leaving the hole there is more diffraction,a large proportion of photons are diffracted (there is less “middle” of the beam for them to avoid being diffracted; by the way it is of course much more compacted than that; but it is a good enough model to have in our heads for us to see what is going on), and the arrows are more widely directed, pointing at more of an angle from the smaller hole than the larger hole (now rather than three almost undisturbed as in the screen at the left, only one goes through unscathed) as there is more hole edge effect (diffraction) for the size of the hole. That is how diffraction works, it increases the smaller the hole.

More diffraction, more range of momenta.

In fact a door in a room diffracts light coming through it and bends it, so light goes around corners just like sound goes around corners. In fact, YOU diffract! But the effect is so small we can not perceive it.

Now with the smaller hole we have even more information about position but less about the momentum. We know with greater certainty where a given photon is likely to be, but even less about what its momentum is. We still know something about the momentum, we are just less certain for a given photon use precisely what it is.


We see this in the graphs. The up axis of the graph (the thin axis arrow pointing up) is the spread of possible momentums, higher up is more momentum. The axis going left to right (the thin axis arrow pointing to the right) is the spread of possible positions. It is simply where the beam is, so where a photon may be found. So the larger our rectangle is up and down, the larger our spread of possible momenta (our uncertainty for a given photon is larger) and the wider the rectangle, the larger our spread of possible positions, (our uncertainty about position is larger).


Graphs of possible states of momentum (up and down), and position (left to right), for the light before it enters the hole (left graph), the large hole (center graph) and the small hole (right graph) .


In the graph on the left, we see a wide spread of potential positions, but a narrow band of momenta. This is the beam before it goes through the hole. So we end up with a narrow rectangle in blue; narrow up and down as momentum is pretty well known (reflecting little uncertainty about the momentum of any given photon in the beam) but very long left and right (reflecting great uncertainty as to just where a photon may be as the beam is wider than the hole before going through the hole).

In the middle graph, we see the situation as the light exits the larger hole. We know less about momentum, so the square is larger up and down, reflecting more uncertainty about momentum due to diffraction and the new direction the light can take. There are now more momenta a photon can have, more directions. New directions means new momenta. On the other hand, we know more about the possible position of the photons because where they are as they exit the hole is limited by the size of the hole, and this is a smaller hole, limiting where they are likely to be, so the rectangle is narrower left and right. We are less uncertain as to where the photon is; it just left the hole so that limits where we are likely to find it, outside of effects like quantum tunneling, a subject for later!


The graph on the right is what happens after light passes through the smaller hole. We are more certain about the possible positions of the photons as this is limited by the smaller size of the hole, so the rectangle is narrower left and right, but we are more uncertain about momentum (more diffraction changing the direction) so the rectangle is wider up and down.

The area of the square and how this area is distributed is the critical thing to look at. Areas in calculus are the “integral,” in this case “integrating” (summing up) our knowledge of possible values for momentum and position in our experimental set up, as it were. Making them squares of one density is too simple of course. The potential state of the photon may not be equally likely to be anywhere in the square. Some states are more likely than others. The likely position, for example, may be more concentrated in the center just opposite the hole. But I wanted to introduce a way to see very important and mathematically sophisticated quantum ideas. The area of the square is the “probability density” of where you will likely find the photon and what its momentum may be in this “space of states,” (that is official quantum jargon) that is, the space, or dimensions, of momentum and position in our experimental set up.

A quantum scientist can never speak about how it “REALLY is” just what is the range of possibilities given your experiment. This relates to integral calculus and Fourier transforms. It relates to the very heart of quantum mechanics. (Congratulations). Much of a course in quantum mechanics is solving such problems of the space of states in a given situation and the areas that reflect probabilities.

These quantum effects, this uncertainty of the “material” world, just like diffraction at a doorway, are real for you and me and cars and galaxies. We can’t see them, as they are very small at the scale of our sensory apparatus (eyes). We think we can look at the speedometer of our car and the direction we are driving and where we are on the road and know both momentum and position, but even there, as soon as we note all that, it has changed. But even if we have a set up that can look at all of this data simultaneously (a whole discussion right there) it would be changing not only because it takes time to observe and note all of these things, a computer can do that very quickly, but because there is no difference between us and the quantum world other than what our limitations as embodied beings relying on sense impressions at our scale imposes.

That is, you don’t know both your position and momentum with 100% accuracy. Just well enough to get through the door (well, and then some).

An interesting implication of this is quite consistent with the Buddhist teachings about change and impermanence. There is never no movement. Not at absolute zero, not ever. If there were no movement it would violate the uncertainty principle. We would know position exactly (wherever we froze the particle) and momentum exactly (no momentum if it isn’t moving!). Really, that’s what I meant at the beginning. This principle is so basic, so essential in the math as well as our observations, that scientists will not allow it to be breached. Like conservation of energy, it is foundational in science.

So what does it mean to me? Is it cool that some aspect of Buddhist philosophy has scientific validation? Sure, I like that, but that isn’t all that important really I think. It also is a taste of the unreasonable ability of math (that was very, very sophisticated math back there) to reflect reality.

And more importantly, as before, it reminds us that what we see, what we can determine about the nature of reality using our senses, is dependent on our limitations, our projections, our assumptions. The concepts, words and intuitions we have developed in the 4 dimensional world of space and time are mere approximations. Don’t get too attached to them. That is what this aspect of the quantum world says to me.


There is no fixed place.


Heisenberg’s Uncertainty Principle!



Right Effort and Conditioning

I was convinced at an early age that I was lazy. I heard it often enough from my mother. And then I heard it from my teachers when I couldn’t be bothered with homework or studying. I bought it. I embraced it.

When my sixth grade teacher told me that despite my over the top standardized test scores he wouldn’t put me in the special program that would allow me to skip eighth grade because I didn’t ever do any work, I had to at least concede that I could see his point. I had long before established my what was then called “underachiever” status.

Cost me a !@#$ing extra year of school, but you know, I had to be me!

But in fact I always did stuff. Even as an underachieving smart-assed kid and teenager. I just did what interested me. While getting mostly B’s and C’s in high school (the only math A I got was in geometry when a substitute teacher challenged me by pointing out geometry was about THINKING! So I actually did the homework and looked forward to the tests!) I took the subway after school to NYU to sit in on a university art history course. I would read Shakespeare and go see Shakespeare in the park in Central Park (it was free!). I haunted the Metropolitan Museum of Art. I was learning ancient Egyptian. I painted and drew.

But to this day I tend to be on the look out. Am I slacking? Were they right? If I stop, if I relax my guard, will I revert to that “lazy kid,” like a once productive cultivated field being reclaimed by weeds?

For that matter, would that be all bad?

Do I honestly think it would all come apart? That the Buddhist “right effort” requires some concept of achieving?

Well, Nyogen Roshi quotes Maezumi Roshi as saying the effort of no effort is the hardest effort you will ever make.


I bring all of this up because I was going to write about very positive experiences I have been having peeling back some of the layers of my medical conditioning. How I am, even now, this late in my game, becoming a bit of a better doctor, a little bit better healer, teacher of doctors and mentor. And I give credit to my practice. And to right effort. I will get into that in another post, but for now I want to note that rather than staying positive, the way I framed it in my mind, the way I was going to introduce it here, was that I discovered that I was intellectually lazy.


I mean, REALLY?

Conditioning. It seeps in very deep.

Mental friggin’ fracking.

Psychic pollution.

Nyogen Roshi says Buddhism is one loud cry of affirmation. Perhaps the first affirmation is to stop calling yourself names.

Quantum Peak Again

There is another famous experiment that I would like to talk you through. I will try with lots of schematic drawings. The pay off is that it is another look at how the quantum world is beyond our day-to-day experience and how our basic notions are projections. For now, that is plenty! We can go deeper later.

We are going to look at what happens when a light goes through an interferometer.

Lets look at the basic set up, a “big picture” look.It is all there, but we will have to go over it step by step. First, what is in the diagram?.



There is a light source, here the green lamp in the lower left corner of the diagram.

The yellow arrows indicate the path the light takes.

There are four mirrors, one at each corner, all indicated by diagonal lines.

Two mirrors, one at the upper left corner and the other at the lower right corner, are indicated by a single blue line. They are full-silvered mirrors and they reflect all the light that comes to them.

Two other mirrors, one at the lower left corner and the other at the upper right corner, are half-silvered mirrors. These reflect half of the light that comes to them, and let half of the light through. A very important point is that the half-silvered mirrors have a front and a back. The back, here indicated by a red line, also reflects half the light and lets half the light through, but there is a change in the reflected light when reflected off the back ( red) side of the half-silvered mirror. The “phase” of the light is shifted. We will get back to that in a bit; it makes all the difference.

The black trapezoid objects in the upper right par of the diagram are light detectors. That is, they will register the light that gets to them (and their color will turn from black to yellow here in these diagrams).

This next diagram shows another overview showing what will happen. We send light through the interferometer and only the top light detector registers light. Why is that? What happened to the light going toward the lower right detector?



Lets follow the light,


Here we see the light that came from our lamp at the lower left in our first “big picture” diagram. This light first interacts with the lower left half-silvered mirror. Half of the light is reflected, and because of the mirror’s angle the reflected light is sent up in this diagram. The other half of the light goes straight through along the bottom left to right. This is why there is a half-silvered mirror here at the beginning of our interferometer device, to split the light into two pants, an upper and lower path.



The half of the light that was reflected straight up along the upper path at the first mirror now reaches the upper left full-silvered mirror and all of that light is reflected, now going along the top from left to right.


The half of the light going left to right on the lower path that went through the first half-silvered mirror next reaches the lower right full-silvered mirror and is reflected up along the right side of our interferometer.



The light in the upper path going from left to right reaches the upper right corner half-silvered mirror. This light from the upper path is again split at the half-silvered mirror at the upper right just like the light was at the first half-silvered mirror at the lower left corner of the interferometer. At this last mirror once again half of the upper path light goes through unchanged, and half is reflected up to the top light detector.



Now here is where it gets a bit tricky. The light from the lower path next reaches this last half-silvered mirror in the upper right corner of the interferometer. But this time it interacts with the back of the half-silvered mirror! This light from the lower path is also split at the half-silvered mirror. The half of the lower path light that goes straight through the half-silvered mirror continues up to the upper detector unchanged. That light transmitted from the lower path gets to the upper detector at the same time as the light from the upper path that was reflected up to the detector, so the light reflected from the upper path and the light that goes through from the bottom path combine and the upper detector registers the light.



BUT the light that was reflected off of the BACK of the upper right half-silvered mirror from the lower path is now shifted 180 degrees out of phase by the back of the half silvered mirror! This means the peaks of this light, the “out of phase” light reflected off of the back of the half-silvered mirror, now in red in the diagram (but don’t get confused, that color change is just to make it easy to follow; the light doesn’t change wavelength or color) lines up with the troughs of the light that went through from the upper pathway.


So the two light waves, the wave of light that went through the last mirror from the upper path and the wave of light reflected form the back of the mirror from the lower path  “cancel” each other out. They completely “interfere” with each other (negative interference in the jargon). Hence the name of the device: interferometer!

The peaks, like we have seen in previous posts and in the diagram to the right here, we can think of as +1, the troughs as -1. So you can see how the +1 peak lines up with the -1 trough, and that kind of alignment of the same + with – holds true throughout the whole wave. So the +’s combine exactly with the -‘s and cancel each other out (+1 and -1 =0).


So NO light gets to the lower right detector, which remains black in our diagram.

When only the upper detector detects light, the lower right detector detects nothing, we know that both paths are open and the light went through both the upper and lower path.

Now for a really amazing result: if we send one photon at a time through, once again only the upper detector registers light! The indivisible, basic particle, the photon say (but other particles and even small molecules have been shown to do this), the discrete energy carrier of electromagnetic waves, is in both pathways. But it can’t be, a photon, a particle, is a most basic thing, it is not divisible, of course.Right?

Well, yes, but no. This situation where the photon interferes with itself when both paths are open is called “superposition.” It almost seems as if the photon is “in” the two paths at once in superposition. This is a mathematical idea, of course. Superposition is a word for a phenomenon that can be mathematically described but has no four-dimensional meaning in any sense we can picture or comprehend based on our day-to-day experience and our monkey brain.

The particle is, in effect, going through all possibilities of all of the paths, every one however unlikely (in this “simple” case both paths are equally likely). Though of course that is impossible in ordinary time and space.

Now, if you block a pathway, then both detectors detect light!  If  you send a beam of light through just one path (either upper or lower;in the diagram below it is the upper path) both detectors register light. If you send one photon at a time through only one path of the interferometer then only one of the two detectors will register each photon that goes through, but over many runs with single photons half the time the upper detector will register the photon, half the time the detector on the right will register the photon!


To see what is happening, in this diagram the upper pathway is open, the lower blocked. At the upper right half-silvered mirror half of  the light (or half of the photons over different run when one photon at a time is sent  into the interferometer) goes through the mirror to the detector on the right, half at the light (or half the photons over different runs) is reflected up to the upper detector.

The situation is the same if the upper pathway is blocked. The light reflecting off the back of the upper right half-silvered mirror is indeed phase shifted as before, but there is no other light wave from the upper path going through the half-silvered mirror to “interfere” with the out of phase light (the detector doesn’t care about the phase), so there is no “negative interference,” No two waves to cancel each other out!

So if both detectors light up when a beam of light is sent through, or over many runs with individual photons, you know that only one pathway is open!

This shows that indeed photons can act as discrete particles that can be detected one at a time. As before with the double slit experiment though we have to ask, how do they “know” to go half the time to one or the other mirror if they are separated in space and time?

Here is the kicker. If you don’t block either pathway, but set up some sort of detector that will tell you which path the photon is on, even if you can show it doesn’t mess with the photon in any way you can tell, it is just as if the other pathway is blocked. The superposition disappears! Both detectors will register light (again, when sending only a photon through at a time they won’t both detect the photon at the same time, one or another will do so, but over many runs it will be half and half again!).

Lets stop here. This is one of the big deals in quantum mechanics. Why does “knowing,” that is detecting the photon on one path or another make a difference? What does knowing or detecting mean? And didn’t we already show the photon is in this weird superposition as if it is in both paths at once?

I told you not to get hung up on how you are picturing this. It won’t work.


Special thanks to Prof. Benjamin Schumacher whose Great Courses lectures on quantum mechanics are very good and who presented this version of the interferometer.

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. Continue reading