Where and When

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

Where does it go?

Don’t gloss it over.

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

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

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

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

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

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

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

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

I say that because, I don’t know.

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

Maybe sometimes not knowing even helps.

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

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

 

Circle Triangle Square and Symmetry redux

 

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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:

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

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          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.

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 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:

 

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            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:

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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.

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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

 

 

 

 

 

No Time, No Space, No Problem

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A riddle:

What is so small that you cannot measure any dimensions, and has no mass; you can fit any endless number of them in one place, yet it can extends across the entire universe with no time elapsing and with no intervening space; that exists in a real sense without space or time, yet it is real and you can experience it directly and your very life, your very existence, is dependent on it?

Maybe a thought fits that description? Or God, if you lean that way? Or Buddha Mind, or the 8th Riki, Alaya consciousness, the Akashic record?

Sure, seems to fit.

Or a photon. That fits, too. Light.

A photon, the force carrier of electromagnetic energy, that also carries energy from fusion reactions between atomic nuclei that occur, say in the sun, fueling photosynthesis at the base of the food chain (well, at least our food chain; other forms of life can depend, for example on thermal energy, for deep sea vents, but one can argue that is indirectly form nuclear reactions in the earths core). The infrared photon that you feel as warmth on your skin, and the higher energy  photons of visible and ultraviolet light that make vitamin D in your skin and gives some unlucky people a melanoma. The particle that powers the photoreceptors of your eye so that you see your loved ones  (well this is more complicated; as Buddhist philosophy makes clear there is sensation but then conception, discrimination, awareness. The photon is how you see your loved one but that is not just a matter of photons and photoreceptors. As cognitive psychology, neuroscience, quantum physics, the Lankavatara sutra and Biocentrism suggest, you project, of course, you are creating your world of loved ones. Well, we also chant in the Heart Sutra: except in emptiness where there is no sensation, conception discrimination, awareness. But I digress).

The photon can detected  in the detector of a double slit or interferometer experiment (though so can objects with mass, protons or electrons, atoms, Bucky balls, etc.) in physics that reveals to us the mysteries of non-locality and entanglement. A particle that is so focused and localized that it can knock an electron out of an atom (the photoelectric effect that Einstein won a Nobel Prize for), but that is just as much a wave without defined boundaries, until it interacts and is measured. A wave that can interact with endless numbers of other waves in the exact same place and time. A particle that can also be stacked in infinite numbers in the same time and place (a “lepton” with no dimensions, no mass).

A photon, the “particle” or basic unit (quanta) of light, does not exist in time or space.

The basic algebra of special relativity is clear and experimentally validated.

In the denominator of the Lorenz equation of special relativity for the effects on time and space for objects in motion (and vice versa; see, for example, the appendix in Biocentrism by Lanza and Berman) there is a mathematical term: the square root of 1, representing the speed of light (c) minus the relative speed of an object of interest (well, velocity (v) relative to the velocity of light, but no difference between velocity and speed here for us; velocity is speed with direction, and here that just says both the speed of light and the velocity of what we are interested in are moving in the same direction)  So, if we take the speed of light to be 1, the speed limit, and the speed of the object is some fraction of 1 (how fast it is moving relative to the speed of light), and that object is also moving at the speed of light (as it would be for a photon), the result is the square root of 1-1 = 0 in the denominator.

Well, you can’t divide by 0, it is not allowed they tell us, so right there we get a mathematical absurdity, as the photon does of course travel at the speed of light, it is light. In any case, any mathematical absurdity notwithstanding, as the denominator approaches 0, that is, the speed of the object approaches the speed of light, the time dilation approaches infinity as one expects when one gets some number over 0. 1 over a very small number is a very large number (1 over 1/2 is 2, that is, 2 halves make 1, and 1 over 1/10 is 10, as ten tenths go into one, etc., ad infinitum, as they say).

At the speed of light a tick to tock for that object, that photon, takes forever. The tick to tock can be any measure of “time,” which means in our experience any regular, repeating event we can observe (a tick-tock of the second hand on your antique pocket watch as the spring uncoils, the swing of a pendulum, the time of orbit of the moon around the earth, the half life of a cesium atom, the days of our lives, etc.). The tock never comes as long as the photon is free to do its speed of light thing.

That is the reason for the “twin paradox” you have probably read about that says that if a twin that goes on a journey in a fast moving spaceship, she is younger than her sibling left behind on earth upon her return. Equally there is a proportional length contraction; the faster moving object is squished. As pointed out in “Biocentrism” page 115, if you were to run across your living room at 99.999999% of light-speed, “your living room would be 1/22,361th its original size…barely larger than the period at the end of this sentence.” Yet to the inhabitants of that living room time and space would not respectively seem dilated and squished. “It’s all good,” they would say, “nothing different here in our friendly little living room.” Same for the twin in the rocket who didn’t age as much as her sister because the tick to tock took longer relative to her sister’s so less ticks became tocks, and who was similarly squished relative to the space experienced by her sister. “All good,” she would say. “Ticks become tocks, and I am not squished. Just as it ever was.”

Well, it’s not that simple; the twin on earth is essentially moving away from the twin in the spaceship just as fast as the twin in the spaceship is moving away form earth, just in the other direction; that’s relativity! The living room is moving just the same as you are, but in the opposite direction. Seems perfectly symmetric, so why don’t both twins or you and the living room have time dilation and length constriction relative to each other? How would that work?

The answer is that it isn’t perfectly symmetric for all entities involved. It is a question of how the system of two twins or the system of you and the living room got where they are: the twin in the spaceship accelerated relative to the twin on earth and you accelerated relative to the living room. The two twins both started in the same place and time but only one blasted off, accelerating into space, and you started at rest at one end of the living pumping your legs as you left off the starting block running. In both cases, the space-travelling twin and running you, used a different amount of energy from the other objects in the system to get things started, to get things moving. So it isn’t a perfectly symmetric situation in either case. [This energy portion can get us to that E=MC squared thing of general relativity and how a massless photon can effect space and gravity, but I digress]

Karma!

Back to the photon! Some small percent of the static on your car radio comes from photons that are almost 14 billion years old, as old as the visible universe we can measure. Yet for an object moving at the speed of light time dilates so much that a tick or tock takes forever. Tick, but no tock, not ever, until it slows down, say hitting your cornea then your lens then your photoreceptor if it is of certain wavelengths, or becomes static on your radio of photons with the energy of about 3 degrees above absolute zero). Almost 14 billion years? No tock, no worries, no passage of time, effectively no time. And space? The photon’s space is squished to nothing. No space. No time no space.

Only objects with mass can experience time and space. An object with mass cannot accelerate to the speed of light because the faster it travels the more the mass, as if it picked up mass with increasing speed like snowball effect in a cartoon as a rough analogy; as the snowball rolls down hill picking up more and more snow and getting larger and larger (ignore momentum and gravitational potential energy decreasing and kinetic energy increasing for the snowball speeding the snowball up for this analogy, maybe better think of you rolling a snowball along level ground, though that image isn’t as much fun or dramatic as a cartoon snowball rolling downhill picking up trees in the process, chasing our cartoon hero). So as an object with mass approaches the speed of light the mass of the object would approach infinite mass and so become harder to accelerate and eventually impossible, making the speed of light an unattainable goal (think of mass as a measure of inertia, i.e. how hard it is to get things going.).

That’s where the Higgs field comes in. That is mass. The moving object picks up mass in the form of Higgs bosons like the snowball above. So maybe Higgs is really the Un-God particle, the particle that gives us gravity, space and time. It gives us the experience of life and death.

No mass, no time, no space. The entire universe is here and now, quite literally for the ubiquitous photon and other massless entities (the photon is not alone, just the one we depend on in our lives on earth), there is no there or then.

So how big is photon, a wave, a quantum field, a particle that is without mass, the smallest thing, if thing it is (it isn’t, of course)? Smaller than can be, as it has no mass or dimension as a particle, yet as a wave it is larger than all that is, as a wave it has no bounds. At the same time, it is neither big nor small, since it does not exist in time or space. This is Indra’s net where all interstices are jewels that infinitely reflect all light instantly. Until it registers in your eye or as static you hear. Then it is in your massive world of the relative, of quotidian experience. Your eye that brings the photon released from a star light years away into temporal and spatial existence, mind creating a world of light! Until then, as far as you and that photon are concerned, the star had no existence in time and space.

Crazy world, huh?

 

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Beware Being Seduced by the Cool in Quantum

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I have written about the fascinating and weird quantum mechanics of double slit experiments and entanglement. Gotta love it!  I will write more about quantum mechanics, time, far out speculations, and I am thinking more and more, along those line about entropy. Entropy is often thought of as a measure of randomness, disorder, and in information theory, ignorance. It seems to be on the one hand trivially statistical and on the other hand deeply embedded in our experience and how energy interacts with energy. Some think it is why we perceive time. More on that later. I have some more thinking to do about that first.

Part of what has inspired me in that direction is a book I am reading now, “Now, the physics of time” by Richard A Muller. I just came to a part where he wrote about the worst theoretical prediction in science, and it was a result of the mathematics of the most beloved and trusted theory, quantum mechanics. It concerns dark energy and the predictions as to whether quantum vacuum fluctuations, the variations in energy and virtual particles demanded by Heisenberg’s uncertainty principle and seen experimentally, could explain the accelerating expansion of the universe we seem to observe. This would be instead of dark energy, a kind of negative gravity that is also quite speculative but would better explain recent observations about the dynamics of space and galaxies at the scale of the visible universe. Well, the prediction of the magnitude of the effect of these quantum vacuum fluctuations on the expansion of the universe was off by 10 with 120 zeros after it. That is one big number! That isn’t just wrong, that is bizarrely, sarcastically, profoundly, embarrassingly wrong.

He points out this has been called the “worst prediction in the history of physics.”

Well, quantum mechanics does describe some things exquisitely well, but there is a reason that scientists in some cases spend their careers on speculative mathematics such as string theory. And while we can’t deny the wonderfully tantalizing hints about reality that quantum mechanics serve up to us, we have to remember it isn’t infallible. It is a reflection of the questions we ask. Ask the right ones, it gives great answers. Ask others, it gives answers that surprise and delight and tantalize. Ask yet others, total nonsense.

And that is my main point! So you don’t get quantum mechanics? Well, you can’t get it! It is at its best a great tool but as fare as understanding reality, mind, consciousness, and who you are, it is still just a peek. A peek that is important because it reminds us that the solid, this and that, this then that, the material, the existence of linear time and space  as we experience it in our daily lives, is not quite how it is, that it is an illusion of our sureness, of the scale we live in.  Now, somehow my last sentence was autocorrected but I liked it! I meant to write “illusion of our senses” and it spit out sureness. OK both work, and maybe an illusion of our sureness is even more accurate!

Anyway, that’s how I approach it. Nobody really thinks science can give us a final answer that is experimentally valid. The energies involved are technically not feasible, but beyond the technical limitations, we are limited by demanding answers that fit our brains. No experiment can get outside “reality” to measure it.

To me quantum mechanics, beyond how it helps us make better toys, is just a hint that what we perceive and measure is not how it really works.

It is kind of liberating. How do you see the universe when you know time and space and the nature of what you perceive is the tiniest slice of the pie and sometimes so wrong it is “not even wrong”? How crazy is it when science leads us to that precipice?

I am not so concerned with all of the interpretations, though I will read about them, share them, and get mind blown by them, but they won’t ever prove anything without some uncertainty because they cant ever be certain. And I don’t think that is just due to technical limitations, but limitations of what we can grasp with our senses, however expanded by technology, as being observations in time in space, defined by time and space, experiments performed in time and space, themselves dicey concepts at best.

But besides being mind-blowingly beautiful, elegant, interesting and of value in reminding us of our limitations, if nothing else, quantum mechanics reminds us how deep and profound and unanswerable by the intellect that the very fact of existence, the very fact of consciousness, at its root, is.

It isn’t permission to think every silly delusion you can come up with is therefor true or has equal probability of being true. But it does mean that it is a wild and crazy universe and allowing yourself the freedom to explore the craziness, to embrace and transcend the craziness, to not be limited by the paucity of data, the lack of imagination, the concrete materialistic linear time and space thinking, and certainly to go beyond the dictates of the metaphysics of scientists who disagree with each other (e.g. string theory anyone? Time and space a real entity? Well, certainly not every scientist agrees!) seems a “reasonable” approach. Not that “reasonable” has all that much traction when we get to the level of quantum mechanics, horrible errors, and unproven theories, whether string theories, multiple dimensions,  branes etc.

We can be liberated by the weirdness, and needn’t be limited by the limitations and definitions of what seems reasonable, which will change from one scientist to another when we are at this level of science.

Note that I am not talking about technical, cool observations like discovering exoplanets, or important matters that can be measured and assessed with the tools of science, like the effect of immune therapies for cancer on the pathogenesis of ocular inflammation, and when seemingly paradoxical effects are seen, as me and my fellow researchers have, understanding what that means therapeutically and for how the immune system works (a current research interest of mine), or for understanding and trying to deal with issues like water use, climate change and other environmental problems (bees, date pollution, health of the oceans, etc, etc.), for example. Deny this stuff at your peril and at the cost of great suffering.

I am talking about how we try to answer the big questions of our lives, and science won’t do that. It can approach it, but never reach it. It isn’t built for it.

At the core, it is about who you are that counts. And while that entails quantum mechanics, it isn’t limited by it.

What is it that  “is”? What is consciousness, your very experience of being, what it is like to be? Is that limited by our senses, by time and space, when time and space are themselves called into question by science?

What really is life itself, beyond a working definition of replication, carbon bonds, information, variation, and handwaving ideas like “emergent properties”?

Cool as the quantum world is, as much as it is our world, there is more, it isn’t the whole story.

Or maybe there is less.

You, however, are the whole story.

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Math Koans

Darwin worm stone

OK, not quite koans, but worth some time if you are so inclined:

Where were the 1 million digits of pi that we have calculated (or for that matter the unending string of numbers that are embedded in pi) before we invented numbers?

Same koan:

Where was the unending number we label “e” that is it’s own differential and integral before we invented calculus?

Similar koan:

For both pi and e, where are all those unending digits now?

Similar koan:

How can there be a square root of -1 when any two negative numbers multiplied is a positive number? We call this number “i” and it is essential in the mathematics of quantum physics that is at the heart of all scientific thinking.

I can go on and on, but maybe you get the point.

 

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Entropy, Ego, What’s the Point?

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Rather than launch into a technical description of entropy and the relationship of energy and entropy lets try this first.

More entropy means more disorganization and more ignorance. Low signal to noise. Less information. Like static preventing the faithful transmission of data. Think of loud static on a radio when you are trying to listen to music on your car radio.

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If I tell you I mixed up the numbers one through ten and put them in a bag, then I picked out two, say a 3 and a 7, all you know about the next one I will pick is that it is not a 3 or 7. So they are mixed up, disorganized, and we have a bit of ignorance about some aspect of that system. Relatively high entropy. If I throw in some letters or blanks into the bag along with the numbers, i.e. static, you are even less able to predict the next thing to come out of the bag!

Now I tell you I ordered the numbers from ten down to one. There are no blanks or letters. I picked out a ten. Next picked will be… nine! Very good. You had little to no ignorance. But I had to put extra energy into ordering the numbers compared to throwing them in the bag. I had to have some way to assure they stayed in order as well. Low entropy, but it took more energy.

Meditation can be seen as aiming for high energy, low entropy. But I am not sure that’s quite true for zazen. You’d have to ask a Zen teacher. Certainly “mindfulness” is like that.

A circle is low entropy. You know everything about it and it took energy to create it (minimally mental energy, in addition perhaps energy to move the pencil or program and run the computer).

Symmetry is not ignorance. True, by definition symmetry is present when you can’t tell something has changed, like someone else spinning a circle while your eyes are closed, so that seems like ignorance. But to do that experiment, you need to know that the experiment was planned and then do it! That’s a lot of knowing, organization and energy!

Information is low entropy. It takes energy to put 0’s and 1’s in some order and that is one aspect of what information is. Ordered dualism.

Meaning is how we interpret and experience information. It is our perspective on it. It is contingent to the max. It is easily colored by our wishes and desires, by our egos.

I just read that the Nobel Prize winning physicist Steven Weinberg, who unified the electromagnetic and weak nuclear forces (along with others, of course; anyway major physics achievement) wrote: “The more the universe seems comprehensible, the more it also seems pointless.”

That seems very nihilistic and depressing. Perhaps that’s how he meant it. If so, somehow he had dealt with it because some four decades after writing that he is still writing books!

On the contrary, that seems very Zen to me. And liberating. It relieves us of arbitrary values and goals. The kind the ego sets up to measure ourselves by, so we can achieve them and reassure ourselves. Except when we don’t.

What ultimate, objective, cosmic, universal, non-dualistic “point” could there be? Any point we could articulate would be a human construct, limited and contingent, a dualistic notion of use in only a very small corner of time and space.

Matthieu Ricard writes in his book “Altruism” that the ego is the crystallization of our identity. He writes that we try to protect it. That’s pretty good, but I am not sure that it is quite right. There is no single anatomic brain space that houses the ego. I think the ego is the process by which we protect our identity. The identity is our sense of who we are based on our conditioning (biologic and psychological, contingent on where and when we are). It is how we organize our sense perceptions and react to them. It is our karma, if you will. It is how we try to make the world comprehensible, to find a point. The ego is the process of having and wanting there to be a point. A point is like a location, a beacon, a polar star that the ego can refer to on the horizon to measure itself and its position by so it can better protect us as we cruise through the world of time and space, the world of the six senses.

So as the universe becomes comprehensible, what we comprehend may not be to our ego’s liking. It may not put our bodies (brains included) at the top of the heap. It may remind us that our limited sensory experience is a pretty pale reflection of the vastness of the universe. Of course comprehensible in this context means the forces of nature. The things physics studies. That which can be measured. It does not mean the whole shebang.

To be clear: I am not suggesting a lack of values. I hope you value compassion. I hope you don’t value your suffering and especially not the suffering of others. I am only suggesting not being seduced into thinking that is the “point.”

Or is it? We can chose to embody compassion, we can aspire to the low entropy high energy state. Is that the “point” of our lives, our minds, the dream, the whole show? Some think so. I admit to liking that view. But maybe that’s the point! It is a goal to like, admirable to be sure, but do I like it because it makes me feel better about myself? Is that my ego protecting me?

No “point”? Perhaps that’s kind of like “ordinary mind is the way.” Or the miracle is chopping wood and carrying water. You don’t need a “point” writ large to the universe to eat when hungry, or to be compassionate. That is the functioning of the universe. What needs to be added? What would be the point?

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Information Is The Dreams Stuff Is Made Of

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Recently Stephen Hawking announced a new theory about what happens to information at the event horizon of a black hole.

Some scientists took him to task. They said in effect: isn’t it a bit of grandstanding to announce such a thing without showing your work?

I like that. Hold authority’s feet to the fire! That is the scientific way!

The question is: why do scientists care?

It turns out to be a question that is basic to the scientific view of how the universe is put together. Leonard Susskind wrote great book about it called “The Black Hole Wars.”

You see, information is conserved.

Like energy over all is conserved, is the same at the beginning of a process as at the end, though not the specific forms of energy (e.g. chemical energy becomes heat).

And most definitely not like entropy. Entropy is not inherently conserved!

Information that is conserved is not exactly the same as “meaning.” It is the possibility of different states. You know, like 0 or 1 in the binary code that the computer uses.

Or the letters of the alphabet. If you see:

LOL

in an e mail you think “laugh out loud.” Heck, you can program a robot to recognize it and make “ha, ha, ha” sounds.

Doest the robot know mirth? Joy? What it is to laugh?

Do you?

Is that information?

No, the idea that LOL means “laugh out loud” is meaning gleaned from information.It is not inherent in the information. We supply the meaning. Conscious, sentient beings do. If someone finds the letters LOL in a message many years from now, odds are it will not have meaning to them. Maybe not in very many years; I understand LOL is going out of fashion already. But it will have information.

LOL could have been randomly generated (a complex thing to do) or it could have been from a program that says: insert consonant-vowel-consonent.

Take a circle. Little information is needed to generate the circle:

  1. a definition (all points equidistant to one given central point)

2. and the variable (the distance).

The circle is symmetric. If you shut your eyes and I spin the circle around the central point, when you open your eyes the circle looks the same. No change. Symmetry.

But the universe has changed. The energy I used to move my muscles to move, say a cut out circle, thus spinning the circle, or by tapping circle moving instructions on a computer keyboard to spin a computer soft ware generated circle, comes from energy stored in my muscle cells.  The cells take glucose and break it down to CO2 and H2O molecules and use the energy released from the chemical bonds to create high energy bonds in ATP  (adenosine tri-phosphate) molecules, then the muscles use the ATP molecules for energy, breaking the ATP phosphate bonds (creating ADP, adenosine di-phostphate and then passing on the phosphate released from the ATP; don’t worry if this doesn’t mean much to you. The details aren’t critical) and thereby changing the energy state in the ATP/ADP/Actin/Myosin structure and thus changing the molecular structure of actin/myosin in muscle to create movement.

This chemical/mechanical process resulted in more molecules with less energy in their chemical bonds than the original glucose molecule, and released excess energy as heat. Also heat is generated by my fingers moving the circle or pressing the keys (friction and the energy of my fingers interacting with the molecules in the paper as I move the paper circle or computer keys as they crash into each other). The change in the molecules and the cells and the infrared photons (the heat released) pinging around create a less organized, higher entropy situation.

So the circle is unchanged, it is symmetric, it is in the same state after we spun it that it was  before we spun it, but the entropy of the universe has increased. We can re-create the glucose molecules, but it takes CO2, H2O, cellular organization and energy, for example in  the complex biological process of photosynthesis. But there will still be the same or more entropy each time we go about making any change.

So even a symmetric situation in the “real world” is not totally symmetric.  Even if we do the circle spinning as a thought experiment, where you don’t actually move the circle, as you did when reading this pretty much, takes energy! The energy of the chemical reactions and electrons moving about in your brain when you think generates heat and entropy.

Which leads us to thermodynamics and Maxwell’s demon.

But I digress; lets hold on doing more thermodynamics and Maxwell’s demon for this post. I will do more on that later.

For now, let’s get back to the idea that in the world of change and movement, the world of the senses (themselves of course information processors) information is conserved. Not meaning, just information.

Meaning is contingent. It is not conserved. It is relational, and generates entropy or uses energy to decrease entropy. Either way, energy and entropy are involved in meaning, playing off each other, perhaps. Energy is conserved. Information is conserved. Entropy is not. Meaning is not.

I find that very hard to get my head around. Why should that be? For that matter, why should it be that energy and information are conserved?

Perhaps it is because those conserved elements of reality were never created and can’t be destroyed, no beginning no end, so how can they fundamentally change?

Meaning is dualistic. It is not conserved. It is contingent on context.

Perhaps the universe at its core IS information. Some physicists think so. Every aspect of the universe that is, well, an aspect, is an aspect because it could have been otherwise (not necessarily just any old otherwise, perhaps a specific set of otherwise consistent with the laws of string theory, quantum field theory, whatever). Otherwise it isn’t an aspect.

0 and 1. Yin and Yang. Duality. That is what physics studies, after all. That is the core of our experienced universe of the senses.

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Remember: information is not meaning, It is not essence, noumena. It is phenomena. It is occurrence.

Information is the dreams stuff is made of.

Meaning is determined by sentience.  Consciousness. Is there silicon sentience? If so, that robot will know mirth. And why not? Why should we be carbon chauvinists? Perhaps the very quantum fields can coalesce in many ways to find mirth.

When communications scientists developed the idea of information, it was to quantify the fidelity of communications. Does a phone message get through ungarbled? Not whether the speaker or her message was coherent. Do the 0’s and 1’s that make up your e mail message stay the same, or are some lost in  the “tubes” of the internet? It doesn’t matter if the email is LOL or a consonent-vowel-consonent randomly generated, whether or not it has linguistic or human intellectual or emotional meaning, if at each slice of time and space there was an either/or, a 1/0, there was information.

I will elaborate later. But I don’t know that I will get past the following no matter how hard I try:

Everything that happens according to scientists does not change the total information in the universe (though you can rob Peter to pay Paul energy/information, more here less there. Shuffle it around. That takes energy if we are talking about information). Information cannot be irretrievably lost.

This relates to symmetry (lack of change in some element of a system even if something somewhere else changes)

This relates to energy.

This relates to thermodynamics: what is likely to happen, and the role of entropy.

There is relationship between entropy and ignorance (another post; this is one of the technical definitions of entropy: how we can know the state of the components of a system) but as implied here, there is a connection between a type of contingent sense of meaning, meaning as we ascribe it to the stuff of daily life, meaning as motivation in our world of the senses, of our karmic experience, that is also part of entropy.

There is an Akashic record. Information in the universe is never totally lost. If you could lose information, modern physics collapses. Ask Dr. Susskind (or read his book!). This akashic record is not about some mystical new age vision of some grey haired old guy writing in a large parchment book with a quill pen somewhere or Santa Clause remembering if you were naughty or nice. In theory you could piece back all of the energy and information transitions and reclaim the original. Sure it may take time and energy without beginning and without end, so our technology may not be up to it.

Perhaps this “akashic record” is the manifest mind of the universe. It doesn’t have to track information back, put it back togeher. Perhaps it is the process, the functioning. It is not dualistic. It isn’t stuck in meaning in things like “LOL.” Maybe that is our dualistic perspective.

The process of oneness, of unfolding, of compassion, that is the flavor I suspect of this akashic record.

It is kind of fundamental and I find it kind of interesting!

 

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Where the Rubber Meets the Road; Lessons From a Busy Month

 

I haven’t written on this website for about a month. I have been doing a lot of reading (non fiction mostly) and writing (trying fiction mostly) while keeping up my practices (medical/scientific and Zen). Very invigorating.

Three themes kept reappearing this month.

First, it is fun to have fun, and to share my enthusiasm, which I often have in abundance, but ego, praise and blame, and the need to “do” sneak in so easily. I set myself up for that!

Second, be careful about the stories you tell, they tend to come true in ways that may be unexpected or in ways that are not literal, but true nonetheless.

Third, when looking at how science describes the way reality functions, whether by studying biology and neuroscience, peeking into into the standard model of particle physics, quantum mechanics, string theory (metaphysics or physics? I am in the camp of those who think the former, but that is for another post), the cosmos as information or hologram, multiverses, multiple layered realities, computer metaphors, or whatever big picture cutting edge science and the various interpretations of science (metaphysics) can offer, it seems to come down to:

Is mind an epiphenomenon arising from evolved brain tissue, itself congealed energy, and that’s as far as it goes, or is Mind primary?

Does Mind arise from energy or is Mind the field in which energy and the organization of energy flows?

Does Mind need another field to maintain it, like a quantum field, or the vacuum with it’s teeming sea of virtual particles and energy without beginning or end, or is Mind a name for the ultimate field that, while still dualistic in a way, is an appropriate term to use because it reflects our experience, that is, is our mind, as we live it?

Is what we can measure and perceive primary or is consciousness primary?

Do we really describe Reality with the tools of the intellect, the mathematics we invent, the changes in energy we perceive with our senses, or do these tools of the mind just provide a great quantitative look at one layer that our monkey brains can handle, at the scale we evolved to live in, even if we push that out very far with very clever instruments and experiments, with the underlying energy and principles arising from Mind rather than the other way around?

Even that is of course a story, a concept, but I think when talking about science and practice, about how it is, that is where the rubber meets the road.

It isn’t whether I think I can prove Mind is primary. That’s exactly my point. It has been said that it is like a fish trying to prove water.

That’s why as busy as I get, and as interesting as I am to myself (I amuse myself greatly though it gets a bit much even for me sometimes), I keep up my practice.

I’m kind of curious.

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

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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.

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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.

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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.

Slide2

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.

Slide2

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.

Slide3

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).

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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!

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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.

Fluid.

There is no fixed place.

Ever.

Heisenberg’s Uncertainty Principle!

 

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Circle Triangle Square

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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 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.”

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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.

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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.

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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:

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

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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.

 

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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:

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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:

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

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

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

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

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

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

Dogen:

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

 

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photo courtesy of Susan Levinson