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.