The Sine and Cosine Waveforms

The main waveform of the Periodic Principle is the sine wave; the secondary periodic waveform is the cosine wave. The sine wave is constructed by placing a unit circle (a circle with a radiius of 1) to the left in a graph that will hold the sine wave on the right. The cosine waveform us constructed in a similar manner, but its beginning is 90 degrees out of phase with the beginning of the sine wave. The cosine waveform represents the potential, decontracted force, while the sine wave represents the manifested, contracted force.

The sine wave unit circle rotates along the x-axis of the graph beginning with the angle between the radius and the x-axis at 0; the cosine unit circle begins its rotation with the circle radius set 90 degrees from the radius. Thus, the sine wave begins with an amplitude of 0; the cosine wave begins with an amplitude of 1. These two waveforms rotate at the same frequency, so their measure will always differ by 90 degrees rotationally. This perpetual difference is called the Phase Angle between the two waveforms. The phase angle between the cosine and sine does not vary.

It turns out that this 90 degree phase difference is very significant. It is the Fourth Primary Principle of the Stream of Creation (Origin and decontracted ground). It is fundamental to the control of energy in general, and it has direct importance in analysis of the periodic nature of the nage-uke relationship in particular.

Aikibojitsu approaches the martial interaction overall as a periodic phenomenon in which nage, instead of regarding uke's attack as an isolated phenomenon, considers it in terms of its periodic nature. Moreover, because the entire rhythmic pattern that binds uke's attack can be determined even if only a small subsection of it is manifested, nage is free to move with respect to the overall pattern in a highly defined and martially effective manner.

In order to mount an attack against nage, uke must first gather energy by which to move. This gathering of resources is marked by a distinct psychological event that occurs within uke immediately prior to uke's physical move. That event is the formalization of his psychological commitment to attack.

Nage has learned through practice to observe (sense) the coalescing of uke's decision. Nage is thus able to take action based upon uke's intent rather than imminent physical action. Nage does not have to wait for uke to actually manifest the building intent.

Observing uke, nage stands silently, grounded deeply within the decontracted. Because the deconstracted is non-differentiated, there is direct contact with uke's origin and center of intent. Nage touches uke not externally, but internally!

Nage acquires and is associated with the phase lead position of cosine through embracing the decontracted position of pure non-resistance. This is key to nage's entire martial strategy.

Uke, through the contraction of the unquestioned commitment to the plane of images, is placed by that commitment into the periodically based lagging phase position of sine.

Nage has taken a decisive lead over uke through means beyond anything to do with uke in particular or even the martial interaction itself. Nage has acquired and perfected that position through self-investigation and through movement away from full immersion and involvement in the image. When nage drops into the grounded, non-resistive position, the optimal phase lead of Aiki comes into being. Absent error, nage will thereafter perpetually lead uke by 90 degrees.

Uke and Nage

Uke and Nage

Exponentials

Exponentials