To simplify our discussions, we define the term "order" to mean an environment with a given number of dimensions. A plane has an order of two. A higher order has more dimensions than a lower order. The term "transcendent" means "to be of a higher order" or "to have more integrated dimensions" (See Glossary).
The preceding analogies demonstrated transitions between lower and higher orders. Simultaneously they provided transitions between visible aspects and their transcendent invisible objects. In the same way we are trying to induce the integrated 4-D space-time environment from its aspects: 3-D space and time. From the observations of waves and particles, we want to transcend to understand the quanta from which they are projected, and so on.
The key to this process is a thorough understanding of the relationship between a whole and its constituent parts. This is an age-old problem that was already debated vigorously between Plato and Aristotle. Plato postulated that the phenomena of our world are only aspects, shadows of invisible real things that he called "eidos" (31). Aristotle instead believed that the phenomena of our world are the real things, and that Plato's eidos were abstractions that lacked true reality in themselves (32). This debate flared up off and on throughout the history of the Western World, and it is not fully resolved yet. This paper attempts to do so, based on our understanding of different dimensional spaces and transitions between them.
Imagine a cut crystal, say a diamond, and consider only its form, ignoring its material (Fig.4). The form represents a whole, while the planes of the crystal envelope are the constituent parts of the whole form. With this we can easily make several observations. They will be very useful for transitions between 3-D and M-D to be discussed later. We shall call these observations "holon principles" and give each of them an alphanumeric number HP1, HP2, etc.. The term "holon" was suggested by Arthur Koestler for the composite of a whole and its constituent parts (33). We shall discuss later whether the holon principles derived from this simple example are universally valid

HP1. *The whole has more dimensions than each of its constituent parts.*
In our simple example, the whole crystal form has three, the parts only two dimensions.
HP2. *Each part is an aspect of the whole, seen from a lower order.*
When we put our mind into the frame of the 2-D order, then we perceive each plane as a separate, individual part.
HP3. *The whole encompasses all its parts.*
The 3-D crystal form encompasses all its 2-D side planes.
HP4. *The whole is invisible from the orders of its parts.*
To the 2Ds, the whole crystal is not visible, because they do not perceive 3-D space. They don't even know about the existence of their fellow 2Ds in the other planes of the crystal.
HP5. *The whole is an undivided and homogeneous entity, while its parts appear as separate individual entities in their order.*
The 3-D space within the whole crystal form is continuous and homogeneous. In contrast, the parts exist as discrete 2-D entities.
HP6. *The whole and its parts are one and the same, viewed from different dimensional orders.*
From the 3-D point of view, we see the whole crystal, and we consider its surfaces as mere aspects of the same thing. From a 2-D point of view, we have discrete, individual planes. Another analogy for HP6 is David Bohm's fish-tank with TV cameras. The important point in holistic thinking is to distinguish carefully between observations made from different orders.
HP7. *Both the whole and its parts are real, but the whole has a more profound reality.*
There should be no disagreement that a 3-D form is more profound than a 2-D plane.
HP8. *The parts are wholes in their own right at a lower order.*
Each plane is an entity of its own in the 2-D order. In turn, the lines are 1-D aspects of the 2-D planes, yet they are entities in their own right within the 1-D order. And so are the points aspects of the lines, but they can also be seen as entities in their 0-D order.
HP9. *The whole is immanent in each of its parts.*
Our 2-D creature analogy is more representative if we picture the 2Ds as crosscuts of billiard balls, as figure 2 shows. They still have 2-D "bodies", but their real self is invisible to them in 3-D space, as ours is for us in M-D space. Asked about the location of their real selves, they would say that they are inside their bodies but transcendent to them. The term used for inside while simultaneously transcendent is "immanent".
HP10. *A change of any part goes simultaneously with a change of the whole, and a change of the whole goes with changes in its parts.*
A change of any crystal plane goes with a change of the whole crystal form, including other planes. One has to be careful here not to assume too easily a cause and effect relationship. From the lower-order environment of the parts we might conclude that one part pushes its adjacent parts around, causing them to change. But, viewed from the higher dimensional order of the whole, the whole is undergoing a change that is reflected in its aspect-parts, perhaps without us being able to say where the change originates. From the whole's point of view, there is no difference between the whole and its parts (HP6). It makes no sense to differentiate between a cause coming from a part or the whole. For instance, when faced with the problem of fitting a crystal into a non-yielding mounting, it makes no difference whether one changes the length of lines, the shape of planes, or the form of the crystal. All goes together simultaneously. More will be said about causality within a holon in section 4.
It is very important to understand how change is transmitted within a holon. Suppose one part changes in some way. This is associated with a corresponding change of the whole. Now, since the whole is immanent in all its parts, they are all affected, their inner disposition is changed, affecting their future trend. The communication between the parts via the whole occurs because the whole is homogeneous, undivided.
HP11. *It is impossible to perceive simultaneously more than one aspect of a whole undistorted from a lower order.*
Assume that we take a photo of a crystal, with the camera film parallel to one of its planes. Only this plane appears with its correct shape on the photo, all other aspects appear either distorted or not at all. The 2-D photo is in a lower order than the 3-D crystal.
HP12. *The holon principles 1 through 11 apply to all dimensional orders.*
The reader may want to verify each holon principle for the case that the crystal planes are the wholes and the lines their parts. Then repeat the same for the lines as wholes and the points their parts. (Note that points can change only their positions). Having established that the principles are valid for all three transitions from 0-D through 3-D, the best assumption we can make is that they are also valid for all higher dimensional orders. HP12 is postulated as a reasonable hypothesis.
HP13. *The holon principles 1-12 are aspects of one master holon principle.*
The holon can be experienced directly, without passing sequentially through the principles 1-12 one at a time. This writer had this experience spontaneously as a young person. It was impossible to describe the holon directly without braking it down into discrete, individual principles. Even then, something is still missing: the homogeneity, the depth, the integrity, the vitality of the holon. The holon principles are an interrelated group. A mathematician might be able to formulate a single expression for the holon, from which the individual holon principles can be derived. We shall apply the holon principles as a "holistic logic" to research the M-D reality.

The holon principles have been stated above using only one simple example. Other examples are those listed in section 2 for the discussion of common sense limitations. Each pair of space-time, energy-mass, etc. forms a holon with its respective whole. As far as this writer can determine, each pair fulfills the cited holon principles, subject to verification by physicists and psychologists, thus extending the validity of the HP's to four dimensions.
An example for holon principle (HP11) is the Heisenberg uncertainty principle, an important cornerstone of quantum physics (34)(35)(36)(37). It states (in one of its versions) that it is impossible to measure both the position and the momentum of an electron simultaneously. (The momentum is a measure of motion). Assuming that the electron exists in a higher order than 3-D, holon principle HP11 makes this same statement. It appears that the Heisenberg principle is a special case of holon principle HP11.
The holon principles provide a plausible explanation for the so-called double-slot experiment that has puzzled quantum physicists. The experiment is well described in popular literature (38)(39). We will explain it here highly simplified. An electron gun shoots electrons against a target screen at some distance, similar to a rifle practice range. Now we place a shield between the gun and the target screen. The shield has two slots next to each other. We shoot only one electron at a time towards the slots. If we cover one slot, the picture on the target screen beyond shows the spot where one electron has hit, as expected. The same thing happens if we cover the other slot. However, if we leave both slots open, the target screen shows a broad interference pattern from two electron waves that come from both slots. We know that electrons can show up as waves. The surprise is that we get two waves from a single electron. How can a single electron go through two separated slots simultaneously? It is like shooting a billiard ball into two pockets simultaneously.
The answer suggested by holistic logic is that the electron is a holon with its parts in our 3-D space, but its whole in 4-D space. Using a 2-D/3-D analogy, suppose two persons observe a low flying airplane through two widely separated holes in a roof. As the plane passes in close proximity, both persons take photos of it simultaneously. Each developed film shows the airplane clearly and unmistakably. But, if we view both negatives together, one on top of the other, there is interference between the two images.
Similarly, the screen in the experiment shows clear pictures of a single electron when viewed separately, but an interference pattern when viewed simultaneously. As the airplane flies by in the third dimension while we are watching it from two positions on the 2-D ground, so the electron flies by in the 4th dimension, while we are trying to figure out how it passes through both slots arranged in 3-D space. We see only two different aspects of the electron, not the electron itself. True to holon principle HP11, no 3-D analogy can accurately describe all aspects of a 4-D situation. The example does not convey that the part and the whole are not separated (HP3, HP6), as the photo and the airplane are. It ignores also that one can change the whole by changing its part (HP10). Another holon example may be seen in the colors of a rainbow, which are integral parts of white light. When white light is sent through a prism, it fans out into different beams of light with the colors of the rainbow, from red through violet. White light as a whole appears physiologically uniform and homogeneous. In physics terms, it covers a certain frequency range of electromagnetic waves. Its individual parts, the perceived colors, have different frequencies and are enfolded in the white light. If one sends the same colors back through the prism in the opposite direction so that they merge properly, one obtains pure white light again. In physiological terms, the prism provides a transition from the whole (white) to its parts (colors) and vice versa. White light has two degrees of freedom: ranges of color and intensity. The individual colors have only one degree of freedom left: a range of different intensities. This example suggests also how quantum physicists "collapse" quantum wave-packages from M-D space into particles (40), as discussed later under Multiple Worlds, Section 4.
Other holon analogies can be taken from the field of information. The words on this page represent holons with the letters of which they are composed; so do the sentences with the words as their parts, the sections with their sentences, and the whole paper forms a holon with its sections. A symphony as a whole transcends its parts, the melodies, and in turn the melodies are holons with the notes in them. In visual arts, a painting from a good artist expresses dimensions far beyond the assembly of its colors on the canvas. One can distinguish the quality of an art piece by the degree with which extra dimensions are expressed through its constituent parts, be it with colors, marble, tones, or words. Thus some modern "works of art" that are produced through an arbitrary mixing of elements cannot qualify as real art. Another example of holons in communication are TV pictures. The electrical signals that appear in time sequence on the screen represent the separate parts of the TV picture as a whole. The reader may want to select his or her examples from the infinite range of holons in our world, from subatomic particles up to the myriad of galaxies (41). It is better not to start with man-made holons, such as machines or organizations; they often do not represent true holons. The following sections will show how the holon principles lead logically and naturally to a model of the universe that encompasses harmoniously the seemingly conflicting world views of science and religion, of Western and Eastern thought, of matter and mind.

The whole of humanity encompasses the characteristics and capabilities of all humans (HP3). Holistic logic tells us that the entity of humanity forms a holon with all humans. Therefore we assume that a humanity-entity exists in M-D space, with much superior reality and capability than ours. We cannot perceive it, yet it is immanent in us. Humanity-entity includes all our characteristics, therefore it has the characteristic of a single individual that pursues its own interests. It is more intelligent than the smartest people throughout history combined. From its M-D environment, humankind-entity perceives interrelationships and potentials that are impossible for us to fathom. It is aware of our thoughts, because its consciousness includes the consciousness of each human (HP3). As it implements its decisions, it carries us along as we do the cells of our body.
This does not mean that we are not free as individuals. Moving along with the humankind-entity is our inborn desire, because the humanity-entity is immanent in us. The humanity-entity is our very essence, our source, our root cause. Expressing it is what we live for. It means unfoldment of our innermost potentials. The desires of humanity are in our hearts. We want what it wants, and we are free when we can do what we want. From the humanity-entity's point of view, it and we are one and the same (HP6). Humanity-entity's will is our inner drive. That is unless we confuse some erroneous notions of ours with the will of our real innermost self. (This is when we begin to lose our freedom). One must distinguish between independence and freedom. We depend on humankind-entity for our very existence, yet we are totally free to express our own true nature, which is the nature of humankind.
The conscious decisions of the humankind-entity dwell in us unconsciously and we experience them as instinct, as impulses. Thus, unless we have cluttered up our mind with wrong ideas, we can trust our instincts and act spontaneously. Then we take advantage of the superior knowledge and intelligence of our inborn humankind-entity. It is like our fingers doing the bidding of our will. They follow the impulses of our nervous system, initiated by our decisions. We can say that they act instinctively, on impulse, spontaneously. Their instincts are aspects of our conscious decisions. They can trust their instincts, because we are vitally interested in their welfare. We can say the same for our own relationship with humanity-entity. This does not absolve us from using our mind and do our best. Humanity-entity depends on us, as we depend on our fingers to do their job.
A change in any human, for instance from experiences, goes with a change in the humanity-entity (HP10), and since it is immanent in all of us, we are all affected through our inner disposition, the mind of humanity-entity. The transmission from one individual to the others occurs because the humanity-entity is undivided and homogenous (HP9). Such interchanges are more pronounced for people who are closer to each other, because they form M-D wholes on a more intimate scale. Because of our immanent interdependence, we carry responsibility for others as well as for us, whether we are aware of it or not. A drug abuser hurts us all. On the other hand, positive efforts of a few can elevate all society, even if their deeds are not known.