The Mathematics of Jujutsu

In the 2nd century B.C. the great Greek mathematician Euclid, said, “The laws of nature are but the mathematical thoughts of God”. Whether we believe in a divinity or not it is interesting that over 2000 years ago Euclid understood how thoroughly mathematics permeates our lives. The foundation of many of the world’s greatest achievements could not have been accomplished without the application of mathematical formulas and principles. The physical laws of mathematics and nature were created by the effects of gravity on the earth and have been in existence since the beginning of time. Over the millenniums many scientists and mathematicians from Euclid to Aristotle, from Newton and Einstein have written about and expanded our knowledge of how mathematics affects our daily lives. The application of their discoveries has changed every facet of our lives.

Mathematics in all its forms has played a part in the discovery and construction or manufacture of everything from electricity to rocket ships and skyscrapers to automobiles. All the physical laws of nature whether gravity or friction, motion or energy can be defined and measured by mathematical formula. Using these laws and the mathematical formulas that explain them engineers build bridges that carry the weight of cars, busses and trucks while at the same time withstand all the pressures of wind, rain and snow. They are able to build tall building that don’t topple or collapse under their own weight or the forces of mother nature. These same laws teach us how to execute a throw, how and where to unbalance, and where is the most efficient use of our strength.

In 1687 Sir Isaac Newton published “Philosophiæ Naturalis Principia Mathematica” one of the most famous books in the history of science and the foundation for the worlds understanding of motion and gravity. Newton’s “ Three laws of motion”, his explanation, formulas and the ability to scientifically measure the role of force, gravity, momentum and friction on any activity leads us to our best and most efficient application of any movement or technique in the martial arts. Using Newton’s laws all the many facets of the martial arts become understandable, measurable, and most importantly explainable. The why, how and where of any technique can be evaluated. They can be practiced and understood from both a mechanical and intellectual perspective. It doesn’t matter if we are talking about the atemi of karate, the nagewaza and newaza of judo, the tenkan of aikido, or the ju of jujutsu, all follow Newton’s laws.

While this does not remove all the obstacles from learning and applying techniques, it can make that path more understandable and enjoyable. Teaching the body how to move, when to move and where to move instantaneously and without thought still requires years of training even when you understand all of these things intellectually. Science, in all its forms, adds to our understanding of why and how things need to be done. It can lead us to the most efficient use of, and application of any technique. It should shorten the length of time it takes for us to understand these things and appreciate the dedication of those who have spent years learning and now teaching and mentoring those techniques. Finally, and most importantly, it opens up the study of martial arts to everyone because if there are any “secrets” in the martial arts, they can all be discovered through time and the science behind each technique.

The Kuzushi of JuJutsu

Jigoro Kano, the founder of Judo, is generally credited with the first real technical understanding of the role of kuzushi, the use of balance and unbalance in the execution of throwing technique. However, this understanding and training in the ways of unbalancing an opponent in martial combat had existed in Japan for at least fifteen hundred years before the advent of judo.

The art of sumai, or sumo as it is called today, was Japan’s first system of empty hand combat. Employing striking techniques and the use of many forms of unbalancing techniques, most historians believe its origins date back to 23 BC. Often used in conjunction with religious or seasonal festivals, sumo’s originally objective was to ‘force an opponent to surrender unconditionally, or to kill him.” To this end sumo developed many techniques and principles which later found their way into numerous styles of jujutsu and more recently judo. Bare chested and wearing only a loincloth, these grappling techniques rely on a true understanding of balance as well as the strength and focus of the practitioner. Throughout the centuries training in sumo has been most martial artist’s introduction into the principles of kuzushi and their subsequent training in the martial arts.

The classical Japanese warrior, the samurai, was trained in multiple arts and weapons, the yumi,(bow) and later the naginata (pole weapon) and Katana (sword) as primary examples. The use of these weapons in combat, sometimes while seated on a horse, required years of training, coordination, an absolute control of the weapon and understanding of one’s center of gravity and balance.

With the advent and use of armor, the art of Yoroi Kumi-Uchi, grappling in armor, a system developed between the 9th and 15th century enhanced the samurai’s ability to fight in close proximity to one another. This system of grappling and locking to each other developed the samurai’s understanding and use of his balance, leverage and mobility to unbalance and ultimately kill or capture his opponent. While not designed as a strictly unarmed system of combat and as several versions of Kumi-Uchi developed as the armor of the samurai changed or was eliminated, the skills and techniques of this art formed the basis for many classical jujutsu styles. It is in these classical jujutsu styles, developed from the 15th century onward, which melded the skills and techniques of the bladed samurai arts with the lessons and understanding of anatomy, balance, motion and leverage learned through the many centuries of practice in Kumi-Uchi.

Without the benefit of a weapon, differences in size, weight, age and skill levels between opponents became more pronounced. These new challenges required a refinement of the fighting techniques and more thorough understanding of the variables which could affect the outcome of a conflict. The importance of natural posture (shizen hontai), mental alertness(zanshin) position (tai sabaki), and distance (ma-ai), skills which were always and integral part of the combat training of the samurai, were reevaluated and modified as classical styles of jujutsu were created.

Many of these classical styles fully embraced the flexibility and pliancy of the ‘ju” in jujutsu. This concept of both yielding and resisting an opponent’s attack, first by absorbing and thus negating its power and then taking advantage of the vacuum created by the attackers momentary weakness is the core of all martial arts. The ability to control, manipulate and ultimately negate an opponent’s attack is at the essence of all martial arts training. While it is this understanding of “ju” which enables a smaller man to defeat a much larger and stronger one and an unarmed man to defeat an attack by someone with a weapon, it is the accumulated wisdom and knowledge of over a thousand years of training and execution, much involving weapons and much by mortal combat, that allowed Master Kano to create judo, and gives the martial artists of today our understanding of kuzushi and all the other variables which form the essence of jujutsu.