1. Understanding the Triad (Active-Neutral-Passive).
2. Our List of Natural, Stable Trinities.
3. Microcosm, Macrocosm, & the Membrane Between them.
4. Choice (Free Will) Enables Management of Dyadic Balance.
5. The Balanced Family Trinity: Father-Mother-Child.
6. (3=4) Transitioning from Three to Four. Stability Begets Creation.

Addition of the 3^rd Element Builds Upon the Dyad & the POV.
By now many have likely realized that each new numerical archetype builds upon, and adds to, the numerical archetype that precedes it. Instead of "peeling away the layers of the onion," we are actually engaged in the opposite act of "building the layers of the onion" from the core outwards. This is a perfectly natural correlation, because the increasing integer numerical values represent the EVOLUTION of CREATION itself! Each new layer builds upon those that have come before it. So as we begin to study 3, we should focus on both of these aspects: evolving through the mechanism of continual creation. How strange it is that the establishments of Science and Religion (up to now) have espoused that the theories of EVOLUTION and CREATION must be mutually exclusive! We have taken this to the ridiculous extreme wherein we only allow our educational institutions to teach one or the other (but not both) of these theories for how humankind came to be! The reality is that they are just another polar dyad.... And the truth of the interplay between EVOLUTION and CREATION is revealed as we seek to discover and understand the force that balances this dyad!

And Now Introducing #3 - The Neutralizer!
The evolution from the number 2 to the number 3 represents the introduction of a neutralizing element to balance the opposing forces and ideas of any polar dyad. The addition of this third element, which is both impartial and orthogonal to the other two elements, results in the creation of a 3-way dynamic. In geometry we state that "any 3 points can define a plane", which forms a stable platform for further creation. This stable platform is the basis from which our own spiritual, psychological, mental, and physical creations can be born. The most visual example of this stabilizing triad principle is the tripod or the three-legged stool: A stool with only two legs can not even be considered a stool, since it will not stand on its own. However, a stool that has four legs can stand on its own but can also submit to wobbles depending upon the flatness of the surface on which it stands. However, a three-legged stool provides precise stability on all surfaces. The surface upon which a tripod stool sits can be flat, or curved, or even spherical, yet it will always stand without wobbling. How's that for physical evidence of how 3 relates to stability? But it is only one of many examples… And the decision you make on whether you believe in the stability of threes only depends upon how many examples you need before you are convinced. Let's begin to look at all the different triads there are in our universe that keep universal creation going.

And Now We Present Our Growing List of Trinities!
We sort of started a tradition when we created our original list of Dyads on Page 2. So we have taken that table of twos and expanded it by one column to create a table of threes below. (And as with the Dyadic table we have also created a standalone table of Triads with the most current entries) Of course, while it is a table that describes balanced groupings of threes, the table itself contains 4 columns. This is simply a reminder of how 3 = 4, which we discuss later on this page. But for now, we encourage you to examine the entries in this table. Compare the same entries here and in the Table of Twos. Use the results of your comparisons as a means to understand how the interaction of the dyadic elements (+ and -) allows for the creation of the 3rd, the neutralizing (0), element or concept.

"Systems Within Systems" Architecture of the Universe Defines a Stable Microcosm-Boundary-Macrocosm Relationship.
The system-oriented, multi-level architecture of our universe provides us the best possible evidence that there are other forms of intelligent life in our universe. You, the human reader, are an integrated system of mind and body, and you consider yourself intelligent. Your CONCEPT OF SELF is what you use to define the boundary of the system you call yourself from all other things and all other systems. Once you define this boundary, you thereby DIVIDE yourself into MICROCOSM (inside your boundary) and MACROCOSM (outside your boundary). In other words, at the moment we designate any system boundary (i.e. define our CONCEPT OF SELF) we simultaneously define all things INSIDE the self, and all of the things OUTSIDE the self. Therefore, we could make the following reasonable claim:

The triadic system model of Subsystem-Boundary-System (Microcosm-Interface-Macrocosm) both defines and permits an infinite resolution of systems in both the microcosmic (subsystem) and the macrocosmic (supersystem) realms.

The drawing on the left illustrates this concept with triangles and sub-triangles. The diagram illustrates a process of systemic decomposition studied and described by Polish mathematician Wroclaw Sierpinski (1882-1969). The resulting fractal image constructed by following the indicated process shown here is called the Sierpinksi Triangle (or Gasket). If we consider a triangle as representing a closed system, we can break down that system into individual subsystems. As shown in the Gasket, this process can go on forever in the sub-triangle direction. Furthermore, one can always view the beginning triangle as a sub-triangle of a larger Sierpinksi Triangle.

There is an interesting result from the process that generates the Sierpinski Gasket. As you continue to apply the rule, the surface area of the gasket continues to reduce. When you assume an infinite number of iterations of the process, the area of the gasket reaches zero. Isn't it interesting how something that started out as symbolizing 3 returns to a state of 0 as the iterative process continues? Follow this link to a neat little interactive web site with a Java-based applet that lets you follow the process of creating a Sierpinksi Gasket.

In addition to illustrating nested systems architecture, the Sierpinksi Gasket also introduces the concepts of self-similarity, scalability/resolution, and recursion. These concepts are very important to understanding how our universe works, and more importantly, how INTELLIGENCE can develop in any closed system. TOL Training will often re-use and re-visit this important fractal image as we begin to learn how triadic elements of our universe interact to create reality (or what we perceive & believe reality to be). But for now, let's investigate the link between nested systems architecture, recursion, and intelligence.

So When is a System Considered to be "Intelligent"?
Armed with the knowledge of how systems combine at various levels, we can begin to witness and understand how our "sub-selves" (microcosmic subsystems) combine and interact, in an integrated manner, to create our total self. Do we consider any of these sub-systems of ours intelligent? We all possess a circulatory system that transports and oxygenates our blood and body cells. Is this system, when you consider it standalone and without the rest of your being, "intelligent"? Most would say no, but we will come to find that it does, indeed, possess a low level of intelligence. What about our digestive system? Is the system that begins with the mouth and ends with the anus "intelligent"? (Some people would even find it funny to see the words "anus" and "intelligent" in the same sentence!) We also possess reproductive systems, and some may claim theirs is intelligent, while others will admit that their reproductive actions might not always be considered intelligent!

However, when we come to the nervous system we might have a harder time drawing the line between intelligence and the lack of intelligence. The nervous system is a system of the body, just like all the previous systems we have described. Yet, we tend to believe that the nervous system is "THE" system that possesses ALL of the intelligence of the human animal. But how can this be when, if one or more of some of the other systems fail, the nervous system will also fail? If the circulatory system fails, the brain dies quickly. If the digestive system fails, the brain dies more slowly, yet it will die eventually. Clearly the nervous system may possess a great deal of intelligence in the form of information from experience. However, the fact that the nervous system cannot exist without other bodily systems reinforces that intelligence is a byproduct of the integration of subsystems into a larger system, which exhibits some higher-lever purpose. Without the body's ability to experience and transmit feelings of pain to the nervous system, the brain could not "know pain." Such a deficiency as this would lead a person to make less-than-intelligent choices with respect to their bodies simply because they would never feel pain. Therefore, one could say that the ability to sense pain leads to a higher level of intelligence of the entire organism through an informed decision process.

Free Will is the Neutralizing Element Used to Balance Creation.
If there is one truth about the universe that overlays all others it is that we choose our own destiny every single day of our lives. We call this ultimate choice our Free Will. If we envision our Free Will as being a product of our mind's ability to perceive and react, we would place the Free Will in sphere #1 on the TOL. In its position at the top of the supernal triad formed by our head, the Free Will at (#1) rules and mediates between the opposing influences represented by (#2) and (#3). The descriptive terms we assign to spheres #2 and #3 are those that reflect all the opposing forces of universal dyads, such as those listed in our Table of Dyads. For example, we could construct a statement of truth about how Free Will relates to the dyadic opposites of GOOD and EVIL. We could say:

"Our FREE WILL rules the balance between GOOD and EVIL."

In a more general sense, we can restate this quote as:

"Our ability to choose gives us the ability to balance universal dyads."

It is most important to highlight the tight link between Free Will and the choices permitted by all universal dyads. Without at least the two opposing choices provided by the dyad, there would be no Free Will (i.e. if there is only one option, there is no possibility for Free Will to exist, much less to choose). However, the purpose of the Free Will is to discriminate amongst and select between the two dyads. Therefore, if Free Will did not exist, there would be nothing to distinguish between the two ends of the dyadic spectrum. To put it another way, by using the example of GOOD and EVIL, we would say that "GOOD" cannot exist without some definition of "EVIL", and vice versa. The element that provides that definition, or distinction, is our own Free Will.

The Family Grouping of Father-Mother-Child is THE "Holy Trinity".
The "nuclear family" is another example that demonstrates the stability of three elements for any creative force. The triad of man-woman-child is a concept that is becoming less widespread in these days of single parenting. Most societies consider the family sacred, and one reason is because of the stability this triad introduces to all of its participants. Now this is not to say there are no dysfunctional families, and nor are we claiming that single parents cannot do a fine job raising children. However, when the "active-neutral-passive" triad of man-child-woman is complete and unbroken, this "nuclear family" creates a stability that allows ALL of its members the time, space, and resources they need to "fulfill their universal will to create." When one or both parents in a nuclear family die, there is clearly upset with those who remain. They must now make due without one of their members who they relied upon for various needs. When parents separate and divorce, the effect is the same: The split of the triadic union affects all of the family members. But once again we point out that this is not to say that they all cannot recover. Their ability to recover is actually dependent upon their willingness to find new stability in their new lives, rather than remaining rooted in wanting to resurrect the failed union.

A Recipe That Honors the Balance of the Trinity!
The US Food & Drug Administration (FDA) has employed a new symbol to teach healthy nutrition which is called the "food pyramid." How wonderful and appropriate that this triadic symbol of stability is employed to help people bring stability and balance to their diets! If we are to consider our entire diet as a "macrocosmic" concern, then one of the "microcosmic" elements of our total diet is each individual meal. While it is an important part of a healthy life to balance your entire diet, it is also healthy (and rewarding!) to balance each meal. We are often told to balance a meal through the inclusion of three major building blocks that we find in the food pyramid: Proteins, Grains, and Fruits/Vegetables. Therefore, in honor of the power of the balanced trinity (and plain old good food), we proudly present the fantastically tasty (and somewhat labor intensive) Chicken Veghetti! Not only is this meal balanced, but it is also economical in that it uses an entire chicken, which is always cheaper than buying the parts already butchered. Additionally, since the recipe includes both pasta and tomato sauce, it works VERY well as a leftover because it will taste better the second time around! Of all the recipes I provide on these web pages, this is one of the best! Try it! You'll like it! And if you think you can improve upon it... Send me the details!

(3 = 4) Four Groupings of Three Continues the Evolution of Creation.
On our previous page in this sequence, we ended our discussion of the dyad by showing how two opposing symbols such as the dot (·) and the arrow (®) can combine in three different ways (e.g. · · , ¬ ®, or · ®). We used this as a symbolic way to demonstrate the mathematical "truth" that 2 = 3. In other words, two distinct and different entities can manifest themselves in three distinct ways. We carry on that tradition here with the diagrams on the left. These drawings illustrate how there are four different configurations for representing trinity groupings of any dyad (· and ®). Here we can see that the equation 3 = 4 has a certain amount of truth associated with it. To enhance our understanding of how MATTER (represented by ·) and MOTION (represented by ®) interact in our complex-yet-simple universe, we have added the corresponding numerical equations to our "Morse code" (· ®) drawings. This association will help us to further solidify the link between universal phenomena and the relativistic archetypes represented by integer numerals.

Each of these four "operational modes of three" illustrated in the diagrams on the left, represent a form of universal knowledge which can be divorced from any particular language. This universal knowledge describes how the interaction of MATTER (·) and MOTION (®) create the complex realities we observe in our physical universe. We have made reference to two of these correlations in the diagrams of (B) and (C). The manifestation in (B) shows two diametrically opposed elements of MATTER (· ·) combined by and with a single element of MOTION (®). This is a symbolic way to describe a DIPOLE and the FLUX that manifests between the poles. This is one specific example of how this symbolic archetype manifests in our universe. Another more general way to consider this "mode of three" would be any two static points in space, with the arrow then representing the motion required to bring these two points together or to traverse between them.

Now let us turn to the equation and manifestation shown in (C) and note how the "message" of the archetype has changed from (B), yet it is also somewhat the same. In diagram (C) we see (pardon the pun) that a single element of MATTER (·) combines with two elements of MOTION (¬ ®) to describe two-dimensional motion of some unique object.
(We point out that we can alternately depict the two arrows acting in opposing directions on the point, thereby representing a "+X" and "-X" configuration, rather than the "X-Y" depiction we have illustrated above.)
We note that both of the configurations shown in (B) and (C) describe MATTER (·) & MOTION (®), but they do so from two different Points Of View (POV).

We have examined the "unbalanced" configurations of (B) and (C) in our diagram, but now let's compare the configurations shown in (A) and (D). The configuration shown in (A) represents a pure triad of MATTER, whereas (D) represents a pure triad of MOTION. However, these configurations represent an awful lot more than just this..... for these two diagrams define the very fabric of the universe around us.

Oh, What Wonderful Things Can Result From Balance & Stability!
We have barely scratched the surface in demonstrating how the archetype of THREE represents and provides for stability through dynamic interaction. Should you choose to pursue further TOL training, you will be introduced to many more wonderful examples of this universal truth through passive learning as well as active (experiential) participation in various exercises. For 3 truly is a magic number. Once you come to recognize the dominating trinity of any given situation, you will then come to possess the "magical knowledge" of how you can change the energy of any situation from one form to another. This will help you in reaching your goals, and maintaining a healthy balance in your life's activities. For once you have created a stable environment, you may then bring forth stable creations within that environment. And this manifestation of creations from a stable environment is where THREE leaves off and where the archetype of FOUR picks up....