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Beautiful Symmetry: As Above, So Below

As the geometer who sets himself
to square the circle and who cannot find,
for all his thought, the principle he needs,

just so was I on seeing this new vision.
I wanted to see how our image fuses
into the circle and finds its place in it...

Dante, The Divine Comedy

I stand six feet tall, roughly two meters. My radius, the distance from my heart to the tip of a finger, or from my navel to a big toe, is about three feet, say one meter. This length, one meter, is intimately familiar to us. It includes the objects within our reach, certainly within our sight, capable of being smelled, lifted, and so on.

We have greatly increased our ability to manipulate our world by creating tools that magnify this reach and our powers within it. Giant levers that mine the earth, great trains and planes that move megatons of material, even, increasingly, robots that visit distant planets or that process necessarily distant hazardous wastes.

Yet we have little familiarity with what is beyond our reach. The pictures from Mars do not familiarize us with Mars the way we are familiar with our favorite stretch of beach or forest hideaway. The medical profession's familiarity with a virus cannot compare with the more intimate knowledge that we may have of our own health. Our almost miraculous tools increasingly bring us more knowledge of the matters outside of us—and inside of us—but we don't feel a growing sense of familiarity or at-home-ness with these worlds.

We might even propose the opposite—that as we accumulate more and more knowledge of increasingly diverse and specialized matters, we feel more alienated. What does a knowledge of, say, the yeast genome contribute to plasma physics, and what do either of these really mean to us? We don't feel ourselves as in relationship to them, we don't feel their presence, appreciate their reality, except in the most theoretical way. Anyone can tell you "we're made up of atoms", but they've never seen one. It borders on faith, only faith in Science this time around, as opposed to faith in Religion.

The purpose of this essay is to explore a principle that should help us relate to the worlds around us—the very great as well as the very small—and so help us interrelate our ever-increasing knowledge to our lives: to be able to place that knowledge where it "belongs".

This is in direct opposition to any kind of modern nihilism in which knowledge is seen as worthless or worse. It is also opposed to knowledge for the sake of knowledge, as that becomes the collecting of information without a point-of-view, which is meaningless.

In our time, humanity, and in particular Western science, has chosen to organize knowledge based on a compartmentalization of disciplines. Knowledge has been divided into various sciences, such as astronomy, psychology, biology, medicine, physics, computation, and so on. But today we see two opposing forces at work in further scientific development. On the one hand, for generations now, we have seen increasing specialization—one is not just a physicist but a nuclear physicist, or not just an astronomer but a radio astronomer and so on. And even these categories are hopelessly broad for those involved in the fields.

On the other hand, and this is relatively recent, we see an increasing amount of cross-disciplinary studies, and more and more we come across such strange-sounding fields as geomicrobiology, and biomathematics. These new fields are partly a type of specialization, but they are a specialization that recognizes the validity of other disciplines and the need for multiple disciplines to work together to explain and explore new findings.

To put things plainly, barring disaster, we are not about to stop seeking and finding more and more about the infinities around us. But we need to find a way, or more probably, ways, to organize and integrate our knowledge, and to relate ourselves to it. This essay concerns a personal attempt to do just that, and it is necessarily organized from a certain point-of-view.

The point of view I have chosen for the construction used in the following is my point of view. Or, more generally, the human point of view—this perceptive being (you) with a radius of one meter sees and relates to the world in specific ways that are a result of relative size. To us, the star Betelgeuse and the carbon atom are infinitely distant "points". We can, and do, collect information about them, but it cannot have the more immediate importance of our blood circulation or, for example, the success (or lack thereof) of my onion harvest.

It is a curious fact that we see as far in as we see out. By "seeing in", I do not mean psychological insight—too often we don't see far in that sense at all—but rather, in the sense of physically looking inside of things, dealing with things that exist on microscopic and smaller scales. We calculate the largest possible size, the size of the universe, as roughly 1030 meters, and the smallest possible size, the Planck length, as 10-31.

But what is even more curious, even normally inexplicable, is the related natures of the very large and very small, and then of the not-so-large and not-so-small, and then of the next largest and next smallest, and so on. This may be, but does not seem to be, an absolute consequence of our perspective, the point-of-view of the human. And yet the quantities, or more correctly sizes, being related in this essay are not chosen arbitrarily, but are chosen specifically by their common distance from our point-of-view which is the one meter human radius. At 10-13, for example, we have the atom, and at 1013 a star system. Each characterized by a relatively permanent and massive center surrounded by orbitals of relatively insignificant size and mass.

The basic plan of this somewhat more ambitious essay is as follows:

With each larger step, we find a smaller basic building block. And this quantitative change corresponds to a qualitative change.

We will look beyond this too, to the galaxies and the subatomic particles, and even consider the universe and that universal particle, the photon, or quantum of action. While this essay can in no way be comprehensive in listing all levels of the universe, it is intended to provide a principle by which much can be understood and related: By which things may, it is hoped, be organized in such a way that the continual input of new knowledge can be integrated and so related to what we already know. Much more than a mere filing system is intended, rather the discovery or recovery of a structure that aids us in understanding each part and its relationship to each other part, to the whole, and, ultimately, to ourselves.

The easiest way I've found to illustrate this great range of sizes in the universe is to use the meter as the measuring stick, and exponential notation to mark the divisions. I draw a line with the human in the middle, representing a radius of 1 meter. Everything to the left gets progressively smaller and everything to the right, progressively larger:

smallest <--------------------------------1 meter-------------------------> largest

I then mark meter measurements on the line like this:

smallest <-----+--------------+-----------1 m------+------------+---------> largest
  ...  10-2 m (-.01m)   10-1 m (-.1m)      101 m (10m) 102 m (100m) ...
and so on, up to the largest, and down to the smallest, known sizes.

What I intend to show is that the objects a certain distance larger than us—say, a planet measuring around the size 107 m—are intricately related to corresponding particles the "same distance" smaller than us, in this case, the molecule, around 10-7 m. To represent this graphically, I'll draw semicircles that connect some of the same distances removed from us:

(image of
nested semi-circles enclosing ranges from human to

The sizes I'll work with are representative, and certainly specific examples can be found to fit the exact size used. But this is not as important as the principle that, say, molecules are a distinct class from atoms, and are of a larger size. And planets are a distinct class from stars, and are of a smaller size. One may not have to work too hard to find some few exceptions, but their relative rarity simply proves the rule.

Finally, what is most interesting to me is how humans relate to this enormous range of sizes they live in, literally worlds within worlds. The correspondence of the micro-world to the macro-world is also echoed in us: We are in the larger worlds as the smaller worlds are in us. So, while we are doing this exercise of mapping the universe, from greatest to smallest, our time would be best spent, I think, to use examples of the objects we are involved in and are involved in us. For example, when we discuss planets and use an example, let us take Earth, the planet that concerns us most. Similarly, a cell might be one of our blood cells, an atom one of our carbon atoms and so on. In this way we keep the subject matter as immediate as possible. And it may help us realize that the point of view this all matters from anyway is the human point of view—our point of view.

Ultimately, the most interesting aspect of these worlds within worlds is connected with the relationship between the smaller and the greater. The key point to realize is that all the smaller worlds discussed are contained within us. And if, as I propose here, those smaller worlds constitute the larger worlds, we have within us representatives of all the stuff, even of all the laws—freedoms and constraints —of the universe.

But clearly "thinking" this, or "knowing" it, is only philosophy. On the fourth way we are equally concerned with practice. So what is the connection practically? The medium between philosophy and practice is theory (I use fourth way definitions here and elsewhere of course). Theoretically, we can penetrate consciously into the smaller, finer, faster worlds within us, and these finer and finer worlds correspond to ever greater and greater worlds. This penetration into different worlds, requires us—our consciousness—to perceive their range of time. This is the nature and result of the refinement of hydrogens, of energies or matters. Finer more volatile hydrogens may give access to finer, more penetrating perception, greater depth of consciousness. But we have to eliminate leaks, handle the energies, refine them and produce more. This is the work of the fourth way: To master ever finer matters and so grow in conscious participation, grow in awareness and right use of ever more powerful and psychologically useful matters.

"Penetration into the subhuman time of cells creates awareness of the superhuman rhythms of Nature, into the time of molecules awareness of terrestrial time, while further penetration into electronic time implies a similar awakening to solar time."
Rodney Collin, The Theory of Celestial Influence

Ultimately what we are is neither matter nor energy, but consciousness. Consciousness that uses matter and energy. Incidentally, here's an interpretation of the famous formula:

                  E = mc2
If c, light, is perception, then c-squared is self-perception, or self-remembering, the technique we use to transform matter (m) into finer energies (E). As we are, our essential mass is fixed—it is our body and the food we eat. Our self-consciousness is almost non-existent, hence our self-generated energies relatively low. We increase our energy, and we refine it, by increasing our consciousness. The mere matter of our food becomes higher energies, receptive and able to respond to consciousness.

The Human Being

(image of man in a circle)

"There is a relation between the hours of our life and the centuries of time. As the air I breathe is drawn from the great repositories of nature, as the light on my book is yielded by a star a hundred millions of miles distant, as the poise of my body depends on the equilibrium of centrifugal and centripetal forces, so the hours should be instructed by the ages, and the ages explained by the hours. Of the universal mind each individual man is one more incarnation. All its properties consist in him."

Ralph Waldo Emerson

Our work starts here, is based here, and all progress is relative to this central starting point. This is like the idea that "The longest journey begins with the first step." Awareness of greater and lesser worlds begins with awareness of this world. At least, any sustained and practical awareness of other worlds starts here, now.

When properly functioning (and it does happen), this is the world of our intellect. While capable of operating with higher energies, it is a big thing to direct it to the matter at hand, and so keep it from squandering energy and developing weird connections or habits that become hard to break. A very good technique to do this, and one often employed in various teachings, is to force the mind to pay attention, whether on counting exercises, listening to something, certain meditations, and so on. The result gained is because of the reduction of wrong work—of course, all kinds of other explanations are given, depending on the teaching. The advantage of the fourth way is in an understanding of what one is doing and why. It is OK to recite the "Jesus Prayer", engage in "sacred gymnastics", perform complicated tea rituals, and so on, but it can be much more powerful if you understand that what you are doing is controlling attention in the particular center involved, and begin to recognize the power of controlled attention. Then think about what might be possible if attention were controlled not unconsciously, that is, not for reasons that have nothing to do with the control of attention but just achieve any result that they do from the control of attention, and think now what it would mean if attention were controlled with a knowledge of its effects, and how they might be best applied. This is an example of how the way of understanding differs from all other ways. No faith, no exercise, without specific knowledge of the functioning being manipulated and why.

Proper use of our common intellect is the proper action at this stage. There are worlds above and below us, and they are accessible to us, not directly by intellect but directly by our physical, emotional, sexual, and higher functions. But we use our intellect as a guide, to help us put our house in order, and one way it can do so is by recognizing its limitations.

Given that, let's talk about other worlds.

On Nature and the Cell

(image showing range of cell to island ecosystem)

Nature is the result of the activity of cellular life and cellular life exists within Nature. The two pictures above—of a coral atoll and some cells—are a graphic example of a similarity of structure, in which the living center is surrounded by a protective barrier.

100,000 meters is about the large end of the scale here. This is an area with a radius of about 60 miles. It is hard to specify exactly what this is, other than about the size you can go without getting a major change in some biologically-determining factor, such as elevation, latitude, annual precipitation, and so on. The Morrisons write in their book Powers of Ten about this size:

"This is the scale of the countryside, more comprehensive than any peak or river, yet with a kind of unity. It is the diversity of the earth which is here suggested."
Philip and Phylis Morrison, Powers of Ten
This large scale of effect of the cell can be seen in the size of coral reefs, coal and oil deposits, grasslands, forests, and any large natural whole.

In another sense, what we are talking about here is a minimum size that allows a full-scale biodiversity. This is about the size of the island of Hawaii, for example. Evolution can proceed on such a scale, and natural disasters are somewhat mitigated by the diversity of life and habitat. A little isolated sand island, on the other hand, could support only a limited variety of life, and that only temporarily—until the next tsunami or drought obliterated life's tenuous grip.

Cellular life seems intimately connected with the use of molecular energies. Indeed, it would seem that the energy source of a "world" or cosmos comes from the world or cosmos above it. Perhaps this is one meaning of Collin's statement:

"Energy comes from above, not from below. The whole thing is in that."
Rodney Collin, The Theory of Conscious Harmony

This "thin film of organic life" directly relates to the molecular/planetary world by forming a certain molecular atmosphere in which it lives, breathes, and dies, modifying the planetary surface that is its home. It is a transceiver, receiving certain energies and transmitting others. Ultimately this engine is driven by light as, ultimately, everything is driven in all cosmoses.

The receptivity of cells for molecular energies or matters relates to the speed of our instinctive and moving functions, how we can analyze something so complex as a fine wine within a moment, or catch a ball so much faster than we can think about it. To some extent, this speed is not too far from us, as we can, with practice, or sometimes just because of certain pressures, observe our own or other's activities operating at such a speed.

Of Planets and Molecules

(image showing range of molecule to planet)

Planets are composed of a wide variety of molecules. While some molecules exist outside of solar systems, it is with the planets that the cooler conditions and relative stabilities exist that allow the countless combinations of atoms into simple molecules, and simple molecules into increasingly complex ones. We can see on the scale of our own solar system a surprising variety in planets and we have every reason to expect that variety to continue to increase as more planets in other star systems become known to us. The nature of this level, above and below us, seems to be one of a range of complexity due to a range of molecular combinations. Moonless Mercury is relatively simple compared to our Earth-Moon system, which in turn is simple compared to a gas giant, say Saturn, with its rings and large number of satellites. Similarly, there is an enormous range in the complexity of molecules due to the combinations of atoms. For example, the relatively simple water molecule compared to a protein molecule. [1]

Suns of Atoms

(image showing range of atom to solar system)

The old image shown here of the atom, while simplistic, illustrates graphically the basic idea or form of this level. The vast amount of the mass of a star system or atom is in the center, and the external particles or planets surrounding it are miniscule in comparison.

It is chiefly atoms, and their charged states, called ions, that determine stars. Conversely, it is stars that create the range of atoms known to us in our table of elements.

With the discovery of the atomic spectrums (the characteristic bands of light emitted by different atoms in an energized state), modern science began to determine not only the structure of the atom, but the atomic nature of the stars. The light from a star, emitted as an atomic spectrum, allows us to determine the type of atoms emitting that light. This has led to increasingly-refined theories of how stars radiate by atomic fusion, and how, as a result, the great range of atoms in the table of elements is created.

This is a basic feature of this idea that the lower relates to the higher—by learning some aspect of the lower world, in this case the nature of atoms, we learn something about the corresponding higher world, in this case the nature of stars. And that is in the sphere of mere knowledge. Ultimately interesting to us is the realm of understanding, or relating experience with knowledge and, for the solar and atomic scales, it must be a very rarefied experience indeed.

Galaxies and Particles(?)

(image showing range of particle to galaxy)

Little is actually known about the origin of galaxies, so I suppose this may serve as a kind of test of this theory, as it would clearly suppose sub-atomic particles to be the defining element of them. I don't really know what else to say, maybe I'll leave it at that, and hope to expand on this section as knowledge or theories become more solid.

Sheets and Strings (?)

showing deep space view of multiple galaxies)

Understanding the behavior of the universe at large depends critically on insights about the smallest units of matter and their fundamental interactions.
Guth and Kaiser, Science, Feb 11, 2005
The largest scale of structure in the universe and the smallest components causing that structure are currently unknown and debates and investigations are active and interesting. Ideas of sheets or bubbles of galaxies on the large scale, and quarks, strings, and so on on the small scale are some of the topics here, and I wait to see how this develops.

The Universe and the Photon

Strange to say, we seem to know more about the nature of the universe as a whole than we do about galaxies and sheets. Or perhaps it is more correct to say we have more developed theories of universal origins than we do of galactic origins.

Simply put, whether in modern science or ancient myth, the universe as we know it begins in light. Scientifically speaking, we can see how the "particle" of light, the photon, defines the universe. The speed of light, postulated as the maximum possible speed, defines the possible size of the universe. And if, as Anderson showed, photons create particles, we see the source of the physical structures of the universe in light as well. [2]

Every thing is in the universe, and light is in every thing.

To return to "the matter at hand", namely our physical being, we need to search out how these cosmic levels of materiality comprise us. Clearly, the finer the matter, the more pervasive it is—electromagnetic energies ("light" or photons) are active in our atoms, the atoms that comprise our molecules, of which our cells are constructed, and ever larger hierarchical groupings of cells combine to create our physical constituents. But how do we perceive these things? Can we be conscious of them?

Certainly, on the scale of cellular conglomerates, we can be aware. We can sense tension in a muscle, an itch on the skin. But it should be remembered that the actual means of perception, of, say, that itch, is electro-chemical in origin, that is, signals are sent from the skin through nerve cells which relay information by electrical impulse internally and chemical (molecular) secretions externally. In that sense, there is little difference between our perception of "light" by the eyes, sound waves in molecular matter by the ears, or cellular structures by our sense of touch. In all cases, what we register is a result of the electro-chemical action of the cells of the nervous system.

Yet we have other means of perception than the sense-based perceptions, but we rarely think of our sex function or our emotional function as organs of perception. We are even less aware of the possibilities of perception in higher centers. It is in these functions that we sense directly the finer materials of the universe, and by means of these functions that we are able to enter the time, or attain the speed, of such perceptivity.

Where do we begin to "climb the ladder" to these higher functions? From where we are, of course, from "Earth", but this starting point is not even at the speed or level of our sense perceptions, it is rather naturally from the slowest function we have—our ordinary intellectual center. Our everyday, but properly working, "mind". We call this H48, or true personality, and it is exceedingly slow compared with any of the other functions. We have, unwittingly, acquired some even coarser "functions", really artificial apparatuses, that "work" with lower energies, H96 or worse, but such states cannot perceive anything real at all and so are worse than worthless—worse, because they convince us of unreal things, such as our own importance, our negative emotions, our fantastic ideas about reality. So one of the first things we have to do with our ordinary minds is develop, plan, and put into action ways to end the wrong work and begin the right work of our organisms. In general, this is called the Work. Perceptions arising from higher functions will necessarily be faster and more subtle. They must be harder to "catch", and so we must learn to recognize them for what they are. And of course we must tune down the noise of wrong work to be able to do so.

The chief means of turning off the wrong work are such things as the struggle with negative emotions (finding reasons not to express them, this has nothing to do with their suppression which is just more wrong work), and struggle with imagination, identifying, inner-considering, and so on; a whole host of practical techniques elucidated in the various teachings of the fourth way, and practiced in real schools. Above all, what is required is the work on self-remembering. Self-remembering which at first seems like nothing because, indeed, there is nothing there, nobody home. If we are to become conscious of higher, faster, finer, more powerful matters, we have to be here in the first place, we have to develop our consciousness from the beginning. It is difficult because we find we have no will to start with either, and we must struggle for a long time to make what appear very modest gains. But it must be this way:

Consciousness does not develop unconsciously, nor will involuntarily.


1 A discussion of planets and molecules would not be complete without mentioning the theory of "planetary" types, which relates to planets and the molecular secretions of our endocrine system. To one who has not verified the seven essence types, there is not much of interest here. But if one has verified this information, it is almost obligatory to try to face the repercussions of such knowledge. Not only is it ancient and profound, it is virtually unknown, This inevitably must lead to thoughts about the nature of esoteric knowledge. But what I want to speak of in particular here is the curious fact that for millennia the seven types were connected with the seven ancient "planets". Why this should be I don't know. Is there some means of perception by which one may verify this directly? Was an ancient knowledge of planetary positions or activities correlated with a more profound knowledge of psychology than exists today?

At any rate we are left with an accurate knowledge of human types, a very curious correlation with planets, and a modern association with the human endocrine glands. It is the minute molecular secretions of these glands which directly determine the characteristics of essence type. These secretions circulate in out blood stream, centered about our heart, as the planets circle the sun.

2 Commenting on the Anderson experiments, Lawrence M. Krauss, in Hiding in the Mirror said:

The fact that particles and antiparticles could be created in pairs from pure energy (i.e., radiation) completely changed our thinking about matter.
It should have, but didn't. But Krauss was referring to the well-known idea that e=mc^2, and not to the descent of plurality from unity.

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