LESSON THREE:

A True Wizard must come to know the world as it truly is before it can actually be seen, and before it can be seen a True Wizard must first be convinced that the world that is known and seen outside now is illusion.

When I was in grade school my small mind was thrust into a state of confusion and wonder with one simple yet extremely profound remark made by Robert Krumm, my best friend Jeff’s father, upon hearing that his 9 year old son has decided to become an astronaut:

“An astronaut? Jeff, listen to me, in outer space there is no up or down. As it is, you barely know the difference between left and right! Forward and backward are fine if someone points you in the right direction and as long you can see where you’re going! Face it! You’d get lost out there, forever! No, Jeff, you keep your ass here on earth where up is up and down is down as long as you got your two feet on the ground!”

How clearly strange his way of thinking was, and how utterly sane! On earth three-dimensional space makes complete sense with respect to up-and-down, but when we step off into that dark region of outer space our concept of up-and-down makes no sense whatsoever. In fact, all our sense of direction, position and even size lose all significance. Without reference points we are left dangling in an incomprehensibly vast and disorienting void of emptiness without obvious station or extension in space. Space as we know it surrenders all definite qualities and characteristics when it is taken outside our own earthly environment, and even more so when it is taken beyond the scope and scale of ordinary human perception. What then is the true nature of this thing we call space?

For most of us unfamiliar with modern scientific concepts, space is simply enough room for this thing or that or enough distance between this person and that person, and not much else. And even when we begin to think about space more objectively we usually tend to conceive it simply as Isaac Newton did, as something that is absolute. Absolute space is thought of as a kind of all-pervading emptiness surrounding a universe of matter, of things. Space, then, is regarded as something that is separate from objects themselves and objects are said to occupy a certain portion of that vast emptiness we call space. Space, here, is the big place we call the universe which is occupied by a multitude of things, including galaxies, stars, solar systems, lunar satellites, and so on and so on.

Unfortunately, there are serious problems with this absolute concept of space, problems that seem to arise when it is confronted by the enigmatic concept of infinity; specifically when we try to take our concept of three-dimensional space beyond the scope of ordinary human perception. We will soon discover that three-dimensional space is actually inadequate to contain the external world and, in many ways, the external world seems to extend beyond it. Ultimately, this lesson will establish that three-dimensional space is not a property of the external world but merely a category of our thought and perception, and the external world itself may possess a fourth or possibly higher dimension of space we can neither perceive nor conceive by any ordinary means.

Modern science, of course, has already determined that the real world may not actually be three-dimensional, and discussions of time as the fourth dimension of space are widely accepted. However, these ideas will be discussed in greater detail later, in Lesson Four: Time and the Fourth Dimension.

We will begin here first by examining our concept of absolute space, the ordinary, most common concept of space.

Space is generally recognized as three-dimensional because it extends in three perpendicular directions from the hypothetical center-point of any object to give us the measurable dimensions of height, width and depth:

Space, then, is often conceived of as a kind of emptiness within which physical objects exist and all things are considered three-dimensional in that they may be measured in cubic inches, feet, yards, miles or cubic centimeters, liters, meters, kilometers, and so on, to calculate volume, a three-dimensional quantity.p It has been noted that the three dimensions of space examined separately possess no distinguishing properties or characteristics that can be expressed in any precise, mathematical way. In geometry they are often differentiated by symbols, such as a1, a2 and a3, but these symbols do not designate anything definite by themselves and are used only for convenience, to separate these three indistinguishable properties that are, in fact, interchangeable:

Symbolic designations for these dimensions, then, are completely relative to one’s own particular perspective. In illustration, of course, the three dimensions of space can be differentiated, but not defined because we can never be sure which dimension is which unless an object is chosen and the perspective decided upon, as, for instance, in this depiction of a box:

In other words, there is no real up-an-down (height), no real left-and-right (width) and no real forward-and-backward (depth). These distinctions remain, as always, a matter of personal psychological perspective and, in a universal sense, they are all the same, without distinctive identities, almost phantom-like. They are the three necessary yet strangely elusive elements of that which we call three-dimensional space.

It may be easy for us to overlook this elusive quality of the three dimensions of space, but we must consider the possibility that this condition might represent a symptom of some psychological structure shaping our perception and conception of three-dimensional space. Therefore, we should proceed to test the soundness of our perception and conception of three-dimensional space and check for logical inadequacies to determine whether or not it is actually adequate to fully contain and explain the external world. And we may do this by taking our concept of three-dimensional space beyond the scope of ordinary human perception in two opposite directions: the infinitely large and the infinitely small.

When we consider the seemingly infinite expanse of the universe, in both a macrocosmic and a microcosmic sense, we find that we have actually uncovered the two major problems with respect to three-dimensional space in its confrontation with the concept of infinity.

The first problem arises with infinitely large quantities, when, for instance, the actual physical form of the universe is first contemplated in terms of three-dimensional space.

When early thinkers first began to ponder the physical form of the universe they decided it must be a vast void of empty space. Since the sphere was the simplest and most cohesive shape characteristic of celestial bodies—stars, planets, lunar satellites, and so on—it was decided that the universe must be like an infinite three-dimensional sphere. However, a problem in logic arose when they tried to reconcile the idea of a spherical form with the characteristic of infinity as complementary physical properties of the universe. The two concepts are incompatible. In other words, they cannot be logically included as two properties of the same universe.

It, of course, seemed impossible to imagine the universe as finite because a finite universe would have to possess boundaries, and the question arose: What could possibly exist beyond the boundaries of empty space in the universe? Nothingness? The concept of nothingness for these thinkers seemed just as incomprehensible as the concept of infinity. Therefore, the idea of an infinite three-dimensional sphere, deemed more reasonable than the concept of a finite universe, was left unopposed for centuries. Unfortunately, it was later realized that if the universe is infinite it could not possibly have a three-dimensional form. In fact, without boundaries (or a surface of some kind) the universe cannot have any conceivable form at all. The hypothetical center-point of the universe from which the three perpendicular lines, or dimensions, of space should supposedly extend can be any arbitrary point in the universe. There can be no actual center, no boundaries and, therefore, no three-dimensional form:

In the face of infinity our most common concept of three-dimensional space is shattered.

There are those, of course, who have theorized the existence of multiple universes beyond the boundaries of our own. However, this idea is even more problematic than a one-universe theory because it infers the existence of a vast universe of finite universes of which ours is only one. Such a universe would still have to be regarded as either finite or infinite and, thus, we are back where we started, with the inescapable and incomprehensible concept of infinity.

With regard to modern scientific thought, the old Newtonian concept of absolute space has been replaced by a more relative concept of space. In this sense space is not regarded as something independent of things. Things themselves constitute space, for there is no space without matter and no matter without space. Space, therefore, is thought not to exist outside the substance of things and, moreover, each thing may possess its own time determined by the intensity of magnetic fields thought to be generated by mass. In this sense, the universe is thought of as a vast collection of things constituting a synthesis of space-matter-time, beyond which there is nothing. As already established, the concept of nothingness is just as incomprehensible as the concept of infinity and, therefore, this relative model of the universe, despite its scientific acceptance, will remain logically unacceptable.

We begin to see here how the human mind becomes trapped in vicious little circles, from infinity to nothingness and back again, with regard to three-dimensional space.

It is interesting to note that the concept of nothingness has been “filled” with an equally incomprehensible concept called Dark Matter. Dark Matter is a mysterious substance mathematically hypothesized to pervade the entire universe, particularly within regions regarded as vacuums of so-called empty space, yet it is both immaterial and imperceptible to the physical material senses (or by any instrumental means whatsoever!). It exists only in the conclusions of mathematical formulae and is supported simply as the only reasonable explanation for discrepancies in the amount of mass required to fill and sustain our current models of the universe. Modern science, it seems, is being forced to reach out into realms of the imagination for quasi-metaphysical concepts like this Dark Matter in order to replace equally incomprehensible, yet impractical, concepts like infinity and nothingness.

The second problem involves infinitely small quantities, that is, those quantities arising from the Atomic Theory and subsequent mathematical discoveries of various subatomic particles composing what modern physics calls matter.

When we take a clump of earth and crumble it in our hands we are left with numerous lumps and grains of dirt that we may continue to mash and grind into microscopic powder-like particles. Theoretically we should be able to break these particles up even further into infinitesimal bits called molecules and atoms which are said to be composed of even smaller particles called electrons, protons and neutrons. At one time electrons, protons and neutrons were believed to be the smallest building blocks of matter of which all things are composed. Much later it was mathematically theorized that they are composed of even smaller particles of matter called gluons and quarks, quarks being regarded as the smallest building blocks of matter possible; that is, until quite recently. It is now being speculated that there may be even smaller particles of matter!

The question that may be asked is: ‘When will this division of matter ever end?’

Actually, from a purely logical standpoint we should be able to continue dividing any existing particle of matter into smaller and smaller parts as long as they are material (or possess mass) and thus still occupy space. In order for a thing to be real it must occupy at least some amount of space. Therefore, any particle of matter, however small, will always have the capacity to be broken up into two parts, and those two parts into four, and those four into eight, and so on and so on, forever.

As we can see, the concept of matter begins to lose substance when descending into the apparently vast world of the infinitely small.

It may be mentioned here that no one has ever actually seen an individual molecule, atom or any of its subatomic particles, and it is generally understood that they are too small to see with visible light. Therefore, they cannot be photographed as material objects and no microscope has ever been made powerful enough to see what these particles physically look like. There are supposed photographic images of what are called “surface atoms” produced using scanning tunnelling microscopy, but these are merely indirect reproductions of images from electrical phenomena, and nothing actually material. And although matter is now regarded as condensed energy and energy as rarefied matter, it is still asserted that even energy must still occupy space, being composed of energetic particles of matter. With regard to modern physics, the materiality of molecules, atoms and subatomic particles is regarded as mathematically and experimentally proven. However, the results of these experiments and mathematical predictions are not proofs of materiality, only proof that some invisible forces exist, whether they are material or not has yet to be proven. Modern physics, of course, has presented attractive, mathematically deduced diagrams of what the structure of the atom and molecule may look like but these are only theory and not first-hand knowledge of their true physical form.

Of course, it is well known that the atom can apparently be “split” and the amazing and devastating results of this phenomenon are fully acknowledged, but the fact still remains that the existence of particles much smaller than the atom and its subatomic particles, such as gluons and quarks, have been mathematically theorized. And since it is believed that there is at least some amount of space constituting the capacity occupied by each of these particles then we must assume that there also exists the possibility that something even smaller may fit into that space, no matter how incredibly small.

This assumption is only reasonable unless, of course, a particle has become so small that it has lost its three-dimensional nature and no longer occupies space. In this case, however, the particle can no longer be regarded physical or material. In fact, it would now have to be thought of as metaphysical!

It may be mentioned here that modern physics has been forced to implement the concept of the point particle. The point particle is an idealized tiny concentration of matter that has no size or extension in space (which, of course, may be thought of as a metaphysical characteristic). The idea of the point particle became necessary in order to justify certain approaches towards measurement and also to conceptualize the elusive nature of infinitesimally small bits of matter, such as gluons and quarks. The point particle has been a very useful concept in physics, but as a literal reality its actual existence is a physical material impossibility.

At this point we may begin to doubt our concept of matter.

The question that may be asked here is ‘What is matter anyway?’

Matter, we say, is the stuff that molecules, atoms, subatomic particles and all things are made of, but what is matter made of? Does it have a color, a texture, a distinctive smell or taste? What is this stuff we call matter anyway?

We of course know what wood is, what earth and stone are and that they have color and texture, a smell and even a taste, but matter as a perceptible, material substance independent of the nature of the wood, earth and stone composed of it seems incomprehensible. In order for us to regard a thing as real, it must possess at least some distinctive physical qualities. We must be able to experience it as a physical thing before we can decide that it is real. Matter as proposed by modern science, however, has no definite physical qualities at all. Matter is simply some unimaginable stuff possessing no conceivable definition whatsoever. The concept of matter, then, proves to be just as elusive and abstract as the concepts of spirit, soul or the life-principle!

It is easy for us to believe that the external world is explained and the physical laws established by modern science have proven quite feasible and practical in this technological world of ours. Predictions are made and all sorts of useful gadgets are invented, but these developments explain very little, if anything, about the true nature of the external world.

Electromagnetism and gravity, for example, have been studied and the laws of their visible manifestations under numerous conditions are expressed as mathematical formulae using experimentally established units, or measurements, of energy or force, giving these phenomena the illusion of physicality and materiality. However, it has never been shown that these phenomena are physical or material in substance at all. We see only the physical material results or manifestations of their behavior in the perceptible world, and not the actual causes, that is, not the actual physical or material nature of electromagnetism and gravity, the true natures of which remain a mystery.

Moreover, hypothetical units or measurements of energy or force are completely arbitrary; they are convenient divisions of space and time that have simply been decided upon for purely practical purposes, for applications, and based solely on visible or perceptible results. They are like the inch of distance or the second of time and, like numbers, they may be infinitely divisible, representing nothing substantial or concrete in the infinite scheme of things.

The powerful results of electromagnetism and gravity are, of course, quite obvious, but we must admit that the true causes of these phenomena may not be physical or material. These causes do indeed exist and they make themselves known as physical material phenomena, just as spirit, soul or the life-principle and mind make themselves known through the physical medium of life and humanity, in actions and consequences, constructive and creative products, society and civilization, and so on and so on.

From all that has been said we may conclude that matter, the stuff that subatomic particles, atoms, molecules and all things are composed of, may actually be metaphysical, as metaphysical as spirit, soul or the life-principle. In other words, the external world and everything in it, the real world beyond our perceptions and conception of it, is really metaphysical in substance, form and function!

It is in this basic idea that mankind has always believed that certain objects and places may be something more than what the physical material senses perceive and that the human mind may imbue these physical material things and places with thought and emotion, with consciousness, whether positive or negative, thus transforming them at their metaphysical roots into charms, talismans and magical effigies, into potions and elixirs, into mystical symbols, icons and temples, into haunted, holy or evil places. Moreover, these metaphysical qualities in physical material things are thought to be detectable at these same roots by our equally metaphysical minds. It is also in this idea that phenomena of mind-over-matter, oftentimes called magic, are deemed possible, for the metaphysical mind may affect things and events at these same metaphysical roots. Moreover, all artistic and creative products, including dance, drama, music and literature, have at their metaphysical roots the thought and emotion, or consciousness, of the people that created them or of those who actualize them now and, if truly inspired, become examples of Great Art, embodiments of what is universally understood by the human spirit and, therefore, timeless.

As would-be wizards, we are required to understand the final and most difficult point of this lesson. The problems posed by infinity in the two opposite directions of three-dimensional space—the infinitely large (in a cosmological sense) and the infinitely small (in a molecular, atomic and subatomic sense)—represent mental boundaries beyond which human comprehension is barred. These infinite boundaries are not physical; they are mental, and the so-called physical material plane is not actually a concrete realm; it is a psychological one limited by infinity above us towards the vast world of the microcosm and infinity below us in the deep world of the microcosm:

We are trapped between these two infinities, in the physical material world of three-dimensional space, not by reality but by our minds.

As would-be wizards, we must also understand that three-dimensional space is not a property of the external world but merely a category of thought and perception, and the real world may possess a fourth or possibly higher dimension of space we can neither perceive nor conceive by any ordinary means. A fourth or higher dimension of space, then, is not another world, not another plane, it is this world, the way the world really is beyond our perceptions and conception of it in terms of three dimensional space, existing here and now and all around us!

We may assert, then, that the hypothetical center-point of the universe exists only within our own minds from which we can imagine the three perpendicular lines or dimensions of three-dimensional space extending outward towards infinity. Three-dimensional space seems logical only in close proximity to us wherever we are at any given moment and apparently fails miserably when we attempt to contain the external world in both a macrocosmic and microcosmic sense (which are, of course, realms beyond the scope of ordinary human perception). Each human mind, therefore, is like a small bubble of three-dimensional space looking outside into a world that actually transcends that space. The shape of the real world, then, is somehow filtered through the surface of this bubble, like a crystal ball reflecting images from the world outside that only appears three-dimensional to us as we look out into this world from inside this bubble. And, thus, our entire spatial conception of the external world is encapsulated within this extremely small, limited bubble of three-dimensional space.

Moreover, this condition of infinity with respect to space in both a macrocosmic and microcosmic sense is merely a psychological symptom of our faulty perception of the external world in terms of three-dimensional space which, as already established, is nothing more than a mental construction. The real world, therefore, is not three-dimensional and our inability to contain the external world as such in both a cosmological sense and in a molecular, atomic and subatomic sense are proofs that this is so.

Consider also this diagram: a circle representing a three-dimensional sphere. On the sphere, extending up and down across its center, is a curved vertical line that better illustrates the circle’s spherical shape:

On this line is a point, halfway down and in the apparent center on the visible side of this sphere. The point represents the human mind or consciousness. The vertical line represents the extent of human comprehension of the external world in terms of three-dimensional space. As we look up, the line represents our comprehension of space in a macrocosmic sense, a line that curves beyond our scope of comprehension towards infinity in that direction. As we look down, the line represents our comprehension of space in a microcosmic sense, a line that once again curves beyond our scope of comprehension towards infinity in this opposite direction as well. Infinity, therefore, may be regarded as a curve of thought stretched to dissolution, thinning out as we lose grasp of reasonable comprehension of the external world in terms of three-dimensional space.

Although quite abstract, the idea behind this diagram of the infinities is quite interesting, especially if we add the other line, the horizontal line we will discuss in the next lesson, Lesson Four: Time and the Fourth Dimension. And that line is the line of time.