Exponentials

In Aikibojitsu, techniques that are based upon exponential contractions are called Exponentials. They are based on, or derive power, from the inherent power of the principle of exponentiality, either in the transformation of the energy state, and/or in exponential spiral form. Exponentials involve manipulation of uke's body in such a way as to put uke's resistance in cntention with the power of exponential structure rather than in contentiona with nage in the particular.

When nage catches uke into a non-linearly changing situation, uke's responses will normally not be simply slow, but slow by an order of magnitude. Uke's interpretation of a developing martial situation is always based on what he sees currently taking place, because his mind, his 'natural' interpretive view, is contracted and linear.

Uke's decisions regarding technique are therefore typically based on linear conceptualization. The explosiveness of changing change (i.e. exponential) is not native to uke's conceptual mind, so if nage presents as moving slowly, uke's conditioning leads him to believe that nage will continue to move slowly. Uke reads nage as slow, and interprets that to mean that if nage is going to move faster, it will only be slightly faster (i.e. still within the limits of magnitude). That the observed slowness could be the "slow" base build of an extreme exponential break is not something that uke would normally understand.

Even if uke were prepared for and therefore able to recognize that nage is running exponentials, it would remain nearly impossible for uke to act appropriately with respect to those exponentials, except with perfect ukemi. It is the nature of a developing exponential that its true post-break speed and power lie hidden until the last moments of the technique, making it impossible to predict with any accuracy when and to what degree a given exponential will pass through transition. When combined with the intrinsic phase-leading position occupied by nage, uke is placed in an extremely difficult situation.