In Aikido, a technique begins with the attacker coming our way with their attack. Aikido's strategic principles dictate that we must respond in synchrony to the attacker, so as the attacker closes, we also move. Therefore, on the first stage of the attack, attacker and defender move in unison, towards each other. Further Aikido strategic principles dictate that we close the distance between ourselves and the attacker, getting inside the focus of the attacker's weapon, in order to disrupt their distancing and timing. This has the effect of weakening them and breaking their balance. Moving into the attack is a principle called irimi, which translates as "enter". Therefore, the first stage of an Aikido technique is termed "Entry".

In the Founder's oral teaching, he states "Enter Triangularly...". The triangular nature of the entry is also a strategic principle, one that governs the defender's movement. Whether the entry had a triangular shape to the geometry due to Shinto's spiritual reasons, or from a purely pragmatic viewpoint, we will never know. Perhaps the Founder recognised a coincidence in imagery when describing the two possibilities, and thus used it to his advantage. We can join the two terms in order to represent the Entry stage with the Triangle.

Once we have entered into an opponent's personal space, where we have avoided their attack and broken their balance, we then proceed to neutralise the attacker's power by various technical methods, and render them defenseless by manipulating their body into a compromised position. We are therefore "executing a technique" on the attacker. There is a wide range of techniques at the defender's disposal here, the choice of which is determined by the nature of the attacker's attack. It is during this stage that the attacker becomes weakened, and the defender gains a strong position through strategic and tactical means...in other words, it is when the tables are turned on the attacker.

In the Founder's oral teaching, he states, "...Execute Circularly...". Once again, a geometric shape is describing the nature of movement. Generally there is a circular nature to the directions the defender moves against the attacker, and the circle also represents a turning, cyclic notion at a more intellectual level. We can thus join the two terms in order to represent the Execution stage with the Circle.

The Finish stage is where the now stronger defender dispenses with the now weakened and defeated attacker. Aikido principles dictate a number of choices one can take in this regard, ranging from the compassionate to cruel, as determined by the situation and the perceived threat of the attacker. These finishes involve pinning/controlling, throwing, striking or escaping, and there is a geometrically Square nature to the movements performed by the defender at this stage. The squareness is in relation to the position of the defender's body to the attacker's body, and an awareness of the four directions within the surrounding environment. The square also possess notions of solidity and strength in its structure at an intellectual level. In the Founder's oral teaching he states "...Finish Squarely.", so we join the two terms in order to represent the Finish stage with the Square.

By viewing the Entry stage as the Beginning, the Execution stage as the Middle, and the Finish stage naturally as the End, it is clear that the sequence of Beginning - Middle - End is synonymous with that of Entry - Execution - Finish.

Transferring this understanding to the geometric symbols discussed in sequence above, we arrive at a Geometry which graphically depicts both the above concepts of linear progression, with what we call the Linear Progressive Geometry.

The Linear Progressive Geometry of the Entry-Execution-Finish Triplicity in Aikido

This sequence of Triangle - Circle - Square now becomes the basic Geometrical representation of a wide range of linear progressive systems. We will use it like a mnemonic when describing and analysing systems of information which depict events occurring in a sequence that can be separated into 3 stages. The terms Entry, Execution and Finish can be substituted by a wide variety of other terms within other information systems, provided they represent relationships which progress from one state of being, or location in space, in a line to further, subsequent states, or locations.

So how can we use this new Geometry in the real world?

Firstly, it gives us a teaching aid for teaching the martial art of Aikido. There are many hundreds of techniques in Aikido, and to the beginner, their intricacy and complexity can seem daunting at first. The techniques are taught for a number of reasons. Firstly, to teach a range of ways to defend oneself against an attacker, and secondly, and perhaps more importantly, to provide the teacher with a vehicle with which to impart the principles of Aikido itself. It is one thing to describe verbally the principles behind the techniques, but for the beginning student to grasp these principles then be able to apply them into physical movement is a completely different task altogether, because the body/brain connection in most people is not established well, and therefore all beginners find starting out in Aikido training very difficult.

By breaking all Aikido techniques down into the same three component parts (and they can be), the beginner will begin to see a pattern arising from the many apparently different and unrelated movements they are exposed to, and this will facilitate more rapid learning of both principles and techniques.

For myself, Aikido training broke many bad habits of physical movement that I possessed, and then it reprogrammed my movement according to its own set of principles and strategies. Through constant and prolonged exposure to the art through regular training, my body not only changed shape and internal structure, but the way I moved to produce power, in fact, the way I tackled problems and thought about things in general became guided by Aikido's principles and strategies.

In effect, this oral teaching of Aikido helped me develop a worldview, or a perspective on the wider reality. Some may call this brainwashing, but in this case, the new perspective that I took on was deeper, broader, and more detailed in every way compared to what I had when I began.

This new perspective then enabled me to view other systems and phenomena in the natural and man-made worlds in a new light. Using the three-fold understanding of phenomena, I began to find that learning other subjects became much easier. In effect, the Linear Progressive Geometry of the Entry-Execution-Finish Triplicity in Aikido provided me with a learning aid for a wide range of new information systems that I subsequently encountered, as I outlined in the Background pages. It is the Geometry which is used to analyse Knowledge Frameworks or Information Systems that describe processes that sequentially develop through the passage of time, from an initial state to a final state.

A few examples of Linear Progressive Geometries:

Yield – Neutralise – Issue (Tai Chi movement)
Past – Present – Future (Time)
Opening – Mid-game – End-game (Chinese Chess gameplay)
Analysis– Trading– Management (Market trading)
Birth – Growth – Death (Buddhist doctrine)
Learn – Practice – Do (Shu ha ri, learning in Japanese arts)
Orientate – Decide – Act (the OODA decision loop of Colonel John Boyd)
Rest – Excitation – Movement (physics)

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