Triplex Unity Theory - The homepage for information on the Triplex Unity Theory

Basic Principles 2 (1 II 3)

Geometries.

All geometries are constructed with a triangle, circle and square. This choice of shapes is drawn from an important oral teaching by the founder of Aikido, Morihei Ueshiba, on a fundamental aspect of Aikido movement and strategy;

"Enter triangularly, execute circularly, finish squarely."

Geometries can describe, or depict, a number of different types of spatial relationships and sequences of events, depending upon the nature of the information system we are applying them to. Naturally, a system of information that describes the passage of time, such as the "Past-Present-Future", will be a "sequential geometry", whereas a system that describes two opposing forces coming together and clashing, such the "Attacker-Defender-Conflict" Triplicity of Combat, is naturally a Geometry that describes spatial relationships.

Sometimes a single Geometry can depict the sequence of events and the spatial relationships of a single Triplicity, such as the Converging and Diverging Geometries (more on them below).

Varieties of Geometries

There are 9 varieties of Geometries, each structurally different in some important way. The different varieties of Geometry do not necessarily define 9 different types of Triplicities, instead they depict 9 different types of internal structure that Triplicities can exhibit. Some Triplicities can exhibit more than one geometry at the same time, while other Triplicities can be transformed from one Geometry to another through a rearranging of the way we look at the subject matter within the relevent Triplicity.

Examples of Triplicities that relate to each of these Geometries will be given in a separate section, Examples. This section is devoted to the structrure of the Gemoetries themselves.

1. The Linear Progressive Geometry

The Linear Progressive Geometry is the basic form of the Triplicity, and it derives directly from the Aikido maxim: "Enter triangularly, execute circularly, finish squarely" . It is horizontal, moving from left to right, as it is how we in the West commonly depict the passage of time, and it is the direction of flow of many written languages, such as English.

This Geometry depicts a sequence of events, or a flow of ideas etc, that evolve or transit from an initial state to a final state, through the passage of time.

There are two other Linear Progressive Geometries, both closely related to this one, a Descending and Ascending version.

For examples or the Linear Progressive Geometry, please see:

1. Entry-Execution-Finish Triplicity of Aikido

2. Descending Linear Progressive Geometry

The Descending Linear Progressive Geometry is a variant of the above, the only difference being that it shows the sequence vertically, downwards.

It generally depicts an hierarchical influence from a position of superiority to inferiority.

There is also a tendency for the progression to be drawn downwards from above, as if some force such as gravity were exerting an influence.

3. Ascending Linear Progressive Geometry

The Ascending Linear Progressive Geometry, like the one before it, is a variant of the Geometry No. 1, the only difference being that it shows the sequence ascending vertically.

It generally depicts a development or change of state from a lower order to a higher order.

There is also the tendency for the progression to exhibit a form of inertia, or resistance to moving upwards, as if some force such as gravity were exerting an influence on it. Therefore, the movement upwards requires some internal form of energy which drives it upwards.

4. Inwardly Converging Geometry.

The Inwardly Converging Geometry is structurally different from the Progressive Geometries, in that it depicts an inward movement from two opposing polarites towards a common centre. The central position, where the two polarities meet, forms the third polarity, which comes about from a mixing of the two opposing ones.

The central polarity, represented by the Circle, while being a third polarity differentiated from the other two, does inherently contain recognisable elements of the other two.

For an example of an Inwardly Converging Geometry see:

Attacker-Defender_Mixed Trilicity of Aikido

5. Outwardly Diverging Geometry

The Outwardly Diverging Geometry is similar to Geometry No. 4 in that there are two directional aspects, however in this case, the there is an outward movement from the central position towards the two opposing polarities.

This Geometry usually represents a centrally balanced state that could if "tipped", swing to either polarity, depending upon the force exerted on it.

6. Cycling Geometry

The Cycling Geometry is an extension of the Linear Progressive Geometries, in that it follows the progression throught the Triangle,Circle Square, however it returns on itself to the beginning, repeating through the process over and over again.

Although the Triangle, or "Entry" position usually represents the beginning of a sequence, in this case there is a seamless flow between each element, like a circle without beginning or end.

7. Oscillating Geometry

The Oscillating Geometry is similar to Geometry No. 6 in that it depicts a flowing, repeating process, however it is structurally different from it, as it represents a change of state that swings from one polar opposite to the other, while passing through the third, neutral polarity.

The central, third state is a cross-over state, where for a moment, both opposing forces are in equal amounts, but the internal force creating the oscillation pushes through this point of balance to the other extreme.

8. Outwardly Converging Geometry

The Outwardly Converging Geometry is structurally different from Geometry No. 4 in that here, all three polar elements of the system are moving towards a common, distant point.

Even though it appears they are producing a 4th point, the three are actually converging to create a singular state.

9. Externally Diverging Geometry

The Externally Diverging Geometry is not technically representing a Triplicity, rather it is a failed System. The three elements of the Geometry are moving in different directions, separating from each other, thereby generating no relationships with each other. Thus it is a failed system.

These 9 Geometries are the important building blocks for the Triplex Unity Theory, and they will be used often when discussing various Triplicities and Unities. It is therefore suggested that, even thought they are simple, they should be carefully understood and remembered for future reference.

Principles 1 2 3