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.

What You Can Learn From Ukemi

Learning any martial art is a very complicated affair. There is the conditioning of the body to withstand the rigors of the training, the education of the muscles in the body to move and react in a very specific and different manner to each and every attack or technique and, just as importantly, the education of the mind to internalize these mechanical movements of the body and to react instantaneously in a very intricate and prescribed manner to any stimulus or perceived threat. And then of course, there is the ukemi.

Of his many contributions to the martial arts Jigoro Kano’s development and use of ukemi in the martial arts is certainly one of his finest. Before Kano, the learning and practice of most classical jujutsu styles was quite dangerous with few safeguards for the practitioners. Techniques and throws were applied without regard for the safety of the person (uke) receiving the throw. Each person being thrown had to devise his own way of falling and protecting himself. This led to many injuries and slowed down the process of learning. Certainly if you were injured you could not learn or practice and if, during practice, you needed to constantly think about how not to be injured, your focus and attention was diverted from what you were trying to learn. This all changed because of Kano’s systematic approach to falling (ukemi).

The overall conditioning of the body that occurs a result of the constant practice of ukemi contributes to an increased sense of confidence and stability in the learning process. As it increases the speed of learning, ukemi also allows the practitioner to focus exclusively on what they are learning and practicing.

The learning processes of judo, jujutsu, aikido, and karate, are all tactile in nature, in that the practitioners needs to “feel” the technique, to feel their center of balance being disturbed, to feel the pain of atemi, and to feel how their body and that of their attacker responds to the changes of movement, angles, direction and balance which occur during the execution of a technique or from the defense of that technique. The ability to create pain, and or a lose of balance, and the subsequent lock(kansetsuwaza) or throw (nagewaza) which results is only accomplished through the “feeling” of both the technique and the results those actions. Proper ukemi allows the practitioners to feel whether a technique would be or is effective in a safe and spontaneous environment.

The ability to learn how and where to reposition your body and that or your opponent or attacker while being attacked is in direction proportion to the sophistication of your ukemi. As we are all uke and tori at one time or another, an understanding of your position in relative space and that of your attacker, and your ability to manipulate those positions(tai sabaki), distance (ma-ai) and balance (kuzushi) require split second adjustments, only possible with the mindless freedom good ukemi brings. There is in every technique, a subtlety of movement which creates a defense from every attack and an attack in each defense. While everything in the martial arts takes time to learn and instinctively feel, the mastering of ukemi eliminates several of the obstacles, both injury and fear, to that process.

The goal of every martial artist is to find for each movement or technique, that moment in time, when position(tai sabaki) and distance(ma-ai), balance (kuzushi), unbalance, and execution (kake) meld together into an effortless and unthinking combination which dominates and defeats their opponent or attacker. It is through the safety of proper ukemi, and the confidence and stability it brings to the practitioner, that the mind and the body are free to discover that moment in time.