Shihonage, logarithmic spirals, and GPS seem like distant concepts.

Yet they all share roots and underlying principles. But let’s proceed step by step.

Shihonage (四方投げ) is a very interesting projection technique found in several martial systems. Commonly studied in Ju Jutsu and Aikido, it is sometimes shown in Judo technical training as well, although its use in competition remains debated due to regulations.

Its explosiveness makes it particularly suitable for quickly learning motor patterns that are functional to the basic elements of self-defense and aggression-management systems.

But why is it so important, and what are the principles behind it?

The name shihonage literally means “four-direction throw,” and its basic form derives essentially from sword techniques. The pedagogical structure is clear: the partner who attacks represents an axis, relative to which the practitioner performs two cuts. In omote, crossing the attacker’s axis; in ura, spiraling around the outside of their line of attack.

In this way uke can be projected (hence the term shihonage) into the four cardinal directions. In other words, mastering this technique strategically allows one to neutralize an aggression by placing the attacker’s body as a barrier between oneself and other potential threats. Here is a good instructional example provided by Durward Burrell and Marcin Hernik:

Performed in its ura form, shihonage offers an intuitive model of the spiral movement typical of many Martial Arts. The presence of spirals in martial disciplines is a widely discussed topic, and has recently been investigated with a scientific methodological approach. The research group coordinated by Dana Vîlcu, a researcher at the Ferdinand I Military Technical Academy in Bucharest, digitally mapped the body movements during the execution of shihonage, and the results were very interesting.

Not only they obtained a three-dimensional model of a spiral-shaped movement, but they confirmed that correct execution of the technique generates a logarithmic spiral in space. In other words, a spherical spiral, also known as a loxodrome.

All this might not interest the average practitioner. However, we believe that the time and resources invested in practice should aim at the full development of the individual, and that a deeper understanding of what we do allows -through constant exchange between inside and outside the Dojo- a transformative growth.

Until the advent of satellite navigation systems, ships and planes had only one optimal option for traveling between two points: maintaining a constant angle between their trajectory and the meridians.

On a two-dimensional map, this appears as a straight line that crosses meridians at a constant angle.

On a globe, this trajectory becomes an arc of a logarithmic spiral. Pierre Varignon was the first to note that in such a spiral, every half-line passing through the pole forms the same angle with the tangent to the logarithmic spiral at any given point.

Only with the arrival of GPS air and sea navigation became even more efficient, favoring orthodromic routes, great-circle curves that require small, frequent course adjustments enabled only by satellite precision.

Shihonage, then, is indeed an incredibly effective martial technique—but it is also, metaphorically, a navigation tool.

Aikido sets out to study technique with almost obsessive care as a tool for analyzing conflict and, therefore, relationship. The so-called “importance of the angle” can be confined to a purely technical matter, but at a deeper level it carries much broader implications.

The execution of shihonage is often problematic for instructors because the average student performs it by accelerating abruptly and finishing by opening the spiral. This not only exposes uke to unnecessary trauma but also prevents the development of the primary martial skill: maintaining prolonged contact within conflict without losing one’s compass.

If this was essential in the teachings of Budo -cultures in which these techniques were learned essentially to stay alive- it should clearly remain essential for us as well. Even if our social context is less extreme, we may not need shihonage to ensure we return home safely every night.

But we do need to rediscover the North Star of our actions. To transform training from repetition into habit, and from habit into attitude. To achieve this, the geometric understanding of form –kata– is an extraordinary tool, and like all tools, it should not be confused with the desired final result.