Pure Conceptuality


Chapter 5: How much is enough?


OK - Launch the canoes. We are well on our way now, passing through some pretty fast rapids, but there is always the reward of a little relief. The geo-structured landmarks are dramatic and clear so, rest assured, that we are on course and oriented nicely. How could we forget the simplicity and beauty of the Tet appearing out of the fog? Four locations in space and six interconnections. Hopefully, what might have been a mystery as to its nature of self-organization, was properly illuminated. The directness and simplicity of comprehension of Tet delivering the octahedron so neatly is certainly a surprising vision. Is it obvious that this is our Giza? Just imagine that half of the octahedron is buried in the sand over there and, behold, a pyramid already majestic in its wonder, revealing itself and literally ready to speak more to us directly. This really is a fantastic excursion.


Initially, we saw the octahedron in the context of the Tet. It was hidden there in plain sight, really. All of the geometries and potentials of its perfect rational expression existed there the whole time (a priori-en-potentia). Nothing actually had to be constructed. We didn’t have any stuff shipped in. We just carefully looked at what is already here. It is a kind of magical experience without the deception; a new magic, exciting in its true nature and exposition.


It is important here to realize that we are charting our journey. This is not a documentary. The map we make is not the trip. The map does record the trip in a way but it is a tool of understanding rather than the experience of the adventure. It is impossible to keep in mind every moving moment. However, it is possible to visualize and understand and examine from different perspectives these prime conceptual realities. So remember as we reference the chart, we are examining afterimages of real and rational conceptual artifact tools. We must realize that these TRUTHS are realized out of time. The expanding wave fronts and spheres of influence are a tool we carefully used to isolate the simplest possibilities. If we let time run, we are overrun with complexity which cannot be visualized. We have so far discovered absolute truth in the conceptual one unit ABs, the conceptual one unit triangle, the conceptual one unit Tet. Where else have we ever experienced the TRUTH? These manifest conceptual truths become self-evident as realized. Having captured these elemental truths, we conceptually re-introduced time at the four equidistant locations of the Tet and conceptually bisected our “unitary” Universe.


In video 4 we introduced the word frequency. It wasn’t explained but alluded to as multiplication by division. Prime Conceptual Universe only becomes non-unitary by division. There is no addition or multiplication. There is no additional stuff to add to anything or to multiply by. But we have seen that we can (within universe) divide our one unit AB into two units. We can divide those units and those resulting units over and over to get astronomically high numbers very quickly: 2, 4, 8, 16, 256, 65536. So there is no lack of large numbers but what do they really mean? Mathematicians deal with them by reducing the big number appearance by simplifying them notationally by powers, so 65536 becomes 256 to the 2nd power or 16 to the 4th power so it is easier to have some sense of being “graspable.” So does it make more sense to start on a trip that we can accomplish, and comprehend or just get lost in the wilderness forever? The primary way to not get lost is to understand without doubt that the WHOLE is realizable and that high numbers are the result of dividing the whole. Looking from another perspective; if we paddle ten thousand strokes and pull over to the shore we have completed a ten thousand stroke trip. If we do that again, we have completed a twenty thousand stroke trip. It is still one thing even though we have divided it into 20,000 strokes or two frequencies of the original 10,000.


The idea of frequency seems easy, but it is a skill we have to develop on this trip like keeping the canoe balanced or controlling it’s direction by the way we paddle. It does not become comfortable and automatic to think in frequencies just because it seems easy. It takes the practice of doing. And we have already experienced it in the bisecting of the unitary AB. In the case of AB, we don’t have a “stroke count.” We just know that AB is sufficient conceptually to accommodate all of the realizations we have uncovered. So to bisect it is irrelevant as to length. we now have two units or two frequencies in our inventory of conceptual artifacts. We have one identical dimension of two iterations or two frequencies. As a result of uncovering this (a priori-en potentia) self actualizing multiplication by division, the octahedron is self-actualized in that very identical AB dimension while the two-frequency (two unit—two iterations of unit AB) Tet embraces and now depends on the octahedron for its structured conceivable existence. All of this is still within our conceptually realized domain.


But a lot has happened! Let’s try to keep score. With our original one-frequency Tet we have four locations equidistant from each other with six unit length relationships between them and we KNOW by self-evidence that this is the primary lowest possible frequency conceptually complete, wholly integrated, completely resolved conceptual containment system. It is the UNITY in conceptuality. (Where else can unity reside?) Tet “condenses” out of all possibilities by reduction to the lowest common denominator of definite realization. That is to say—Tet is the limit case end point of the outside of time model of manifest potential. It expresses the unification of dimension. It defines one containment of space by one unit of time. It is purely conceptual and expresses four iterations of location and six unit time relationships between the four locations. Those four and six represent in concept, the “frozen” length of time and shape or general representation out of which further self-actuated rational realizations (truth) precipitates. The division of unit length becomes the concept of frequency. Unitary space at minimum has ten considerable aspects. (four equidistant locations and six linear interrelationships) Unity is complex, however it is wholly conceivable in this conceptual model. A one unit (one-frequency) Tet contains one unit of space with one unit dimension of length. Mathematically, that is 1 to the 3rd power = 1 unit containment of space.


Multiplication by Division of Triangles
Let’s explore frequency in terms of our purely conceptual one unit triangle. It conforms perfectly with the idea of frequency. One-frequency (1F) = one triangle (△). A two-frequency triangle contains four one-frequency triangles. Draw a triangle. Divide the three one-unit lengths by putting a dot in the middle of each. Now connect the dots. Get it? Four unit length triangles are definite. Now continue halving those lengths with midpoint dots and connect them. You get 4, 9, 16, etc. In other words, frequency to the 2nd power equals the number of one-frequency triangles “contained.” That is very neat isn’t it? Remember that even if we use conscious license to imagine the triangles to have structured existence, only each individual one-frequency triangle would define flatness or planar existence. Do you see that if you “tried to pick them up,” they are hinged in three directions? They could be waved like a flag. We have to practice what we are learning or we will miss the point. The triangle is a conceptual artifact with context but no content. The Tet, on the other hand, has context and content. You can “get inside” of it and look around. It depends on what point of view you are looking from but you will “see” some of its aspects no matter what your perspective. To see the whole thing you would have to be outside of it and we have no means of doing that yet other than using conscious license. The Tet expresses a full conceptual existence as does the octahedron. We can conceptually feel and touch the Tet or octahedron but we cannot truly grasp the line or triangle. The “line” conceptually represents (time or length) ; the triangle conceptually represents, (time and flatness); the Tet represents time, flatness and containment (space).


These conceptual artifacts are like chess pieces. Each one has a form and brings with it a utility different from the others. Unlike chess pieces, the utility is self-expressed in the self-manifestation of the form. Once defined, the shape of chess pieces represents a hierarchy of function and power based in ultra-high-frequency cognition of the story characters, queen, king, knight and pawn. There is a beautiful geometric game potential which results from the application of the rules over the checkerboard matrix. The pieces just sitting on the board, suggest nothing other than ornaments. With understanding, each finished MOVE sets up a new stopped time geometry. In a sense, chess is a journey from ultra-high-frequency complexity to the ultimate simplicity of being the “last man standing.” As we look around we are surrounded in every nuance by the chessboard and characters in the game of high frequency complex interaction with each other. Our journey is to uncover the very nature of all of this complexity in time and space. We are looking at the board and the pieces all the time hidden in plain sight. We are allowing the whole to reveal itself. We are the pieces engaged in the game looking for the chessboard and the rules. Seeing the chessboard, knowing the characters and even knowing and understanding the rules, in no way eliminates the endless possibilities for adventure, even within the relatively simple proposition of the chess game. A master of chess is a description of a self-aware consciousness who has a knowledge, an engagement, familiarity, experience and comfort with the game. We have a similar goal on this journey.


mathematicasVisuales image of Octahedron in Two-Frequency Tetrahedron
Octahedron in Two-Frequency
Tetrahedron (from mathematicasVisuales)

fdecomite image of Octet Star
Octet Star (from fdecomite)
Now that we are familiar with frequency we can look at our one-frequency octahedron and see what it reveals. First of all, we see that the Tet hides and reveals the octahedron. We won’t go through all that again; just look at the totality. The octahedron has eight triangular faces of unit length one. Thus the name octahedron. In its initial manifestation in the Tet we can see that four of the faces of the octahedron have tetrahedrons of one-frequency face bonded on. These four tetrahedrons are the points of the overlying two-frequency Tet. When there are one-frequency Tets on all eight faces of the octahedron, we have the octet star which we saw in video 4.


The beauty of these conceptions is the whole number rationality of the progression and regression in the scales or dimensions revealed. It is easy to see the number validity of the 2-, 3-, 4-, 5-, 6-, … frequency triangle conforming to frequency to the second power giving the number of one-frequency triangles (areas) contained. Amazingly, volumetric rationality with whole number integrity holds with the Tet as well. So, frequency to the 3rd power is the rule for the Tet. It is more amazing with the Tet as we discover the beauty of rational whole number all space filling with the primordial complementarities of the one-frequency Tet with the one-frequency octahedron. The volume of a two-frequency Tet is 8 unitary Tet volumes (2 to the 3rd power or 2³=8), three-frequency Tet volume = 3 to the third power or 27 (3³=27), and so on. In the conceptuality5 video we will see how that works.


All of the connections and realizations we have observed so far are in one equal whole unit dimension. We have only concerned ourselves with equi-distant, equi-length vectors or trajectories. The technical name for this rationalization of space is vector equilibrium or isometric vector matrix. The mechanical and architectural name for this matrix is octet truss. In Pure Conceptuality this isometric state exists in stopped time (all energy of motion removed). This could also be called the absolute zero state. All conceptual complementarities are in perfect balance.


The point of all of this is that we don’t describe the universe in words and mathematics, the universe displays itself and displays the mathematics in its own rationality and self actualizing interrelationships. We learn the concepts and possibilities of math from the triangle, which is an ACTUAL computer. So, like all academic science, math does not explain; it describes. Math is a highly specialized language, so those of us who do not speak it assume something can be said with it more sophisticated or even almost secret. The secret is there is no secret and we can just look with our own eyes, if we open them to see in a clear and fresh way.


We will see in Video 5 that these self-generated conceptual artifacts describe themselves in whole unit rationality with relationships which are elegant and easy to grasp. We are keeping careful track here so we all feel comfortable as to where we are. It isn’t rocket science! We will get through these mapping lessons. This is just a necessary part of this journey and helps us like 3D glasses at the movies to experience more fully and see with new eyes. There are some amazing things ahead. Now watch Conceptuality5 on YouTube for the visuals of this section.


Commentary on video 5 – In this video the presenter stated, when folding the square, that we had an equilateral right triangle. If you think about it, there is no such thing! But the truth of what it is, is an isosceles right triangle having two equal lengths and a right angle. The hypotenuse is the square root of two. This is another clear example of forms speaking the truth while the presenter's “error” is the context for that truth. It is interesting to note that while folding that triangle, there is a moment where the two moving points are exactly one unit apart. At that moment the Tet formed is one quarter octahedron and has a volume of one-fourth of the octahedron volume or one tetrahedral volume. More truth.