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.

The Nature of Kata

In the 11th century, Shinra Saburo Minamoto no Yoshimitsu, a samurai commander and relative to the emperor of Japan made detailed studies of human anatomy and physiology by the dissection of battlefield dead, convicts and prisoners of war. The purpose, of course, was to gain a better understanding of the mechanics of movement and the ways to which any weaknesses in the bodies anatomy or physiology could be exploited on the battlefield. To take advantage of this new found information and to be able to test theories of movement, new techniques and the best way to apply them, the samurai developed prearranged forms, or kata, which allowed them to practice, using a wide array of weapons, without being seriously wounded or killed.

Each Samurai family (clan) developed kata to teach their particular style (ryu) of weaponry. These family movements and techniques were protected and kept as secrets, taught only to those within the clan. The theory being that if someone had never seen your particular movements, attacks, counters or techniques they would be at a loss or disadvantage in defending themselves from them. Thus, the original purpose of kata was to teach men how to kill, and how to become skilled enough not to be killed. Kata was designed to demonstrate how to attack, where to attack, and when to attack. It teaches how to protect your self from an attack and how to counter an attack. As both sides (uke and tori )know and eventually understand both the attack and its defense, kata provides an invaluable teaching tool and the foundation of all martial arts. The design and practice of kata will protect and forgive the mistakes of both the attacker and defender. As each side practices both attack and defense, they learn the strengths and weaknesses of each technique, as well as each other’s strengths and weaknesses. Because kata allows an individual to practice the same movement or technique multiple times with people of all ages, sizes and weights, kata gives the practitioner the ability to experience how those different variables influence both the attack and their own ability to respond to those differences.

Kata is taught though a series of instructions divided by levels of both experience and knowledge. The relationship between student and teacher (sensei), between those who are more advanced and those who have just begun, builds both respect and humility. By teaching the simpler and less complex movements first, kata slowly conditions and changes the way its practitioners move and think. In this method of training, where each new technique or movement is built upon the accumulated knowledge and skills of the previous technique, kata builds concentration and focus. Over time the reflexes and understanding of movement needed to complete each technique is developed. Through this constant repetition of movement, kata builds confidence and the calmness which allows the practitioner to attack or respond to any attack without thought or reflection, without hesitation or fear, with focus and determination.

Through kata we learn the essence of each technique, we refine our own movements, and learn how to apply the principles of distance(ma-ai), balance(kuzushi) and body position(tai sabaki) to our own techniques. It is only through constant practice and attention that our bodies learn and internalize the many different variables that come into play each time we are confronted or attacked and how to respond to them.

The Nature of Kuzushi

For most of us balance is not an issue. We wake up in the morning, role out of bed, put our feet on the floor, lift our bodies up and begin to walk. If we are healthy and our inner ear is functioning properly, our bodies internal gyroscope finds our center of gravity which gives us our sense of balance, our muscles and limbs find their coordination and strength and we proceed to move and walk an continue with our daily activities.

While we take our sense of balance for granted, our bodily immediately knows and feels when it is out of balance and in danger of falling. It tries to transmit this information to us almost simultaneously and if successful, we are able to reorient ourselves, compensate and take some preventive measures, like taking an extra step or grabbing on to something or some one, before we actually fall. Our ability to stand erect and remain balanced is one of the true gifts of our anthropological evolution. There is however a moment, a second, when we, or our bodies are not really sure if we can compensate, if there is enough time to compensate or how to compensate for being unbalanced. It is that moment, when the body is unsure of what to do, when it is vulnerable, that we wish to exploit.

When we stand and walk naturally we are centered and in balance. Our bodies maintain this balance through a complicated series of communications between our eyes, ears, limbs, and brain. If the interplay between the organs is interrupted for even a moment the brain must relay this information back to our muscle and skeletal system in order for it to make the necessary adjustments, lest we loose our balance and fall.

To attack or be attacked requires the body to make multiple adjustments to this, both delicate and sophisticated system, in order to maintain our strength, center of gravity and balance. The breaking of our opponents or attackers center and thus his balance while maintaining our own is the essence of kuzushi. The act of breaking an opponents balance, their equilibrium, to take or replace their center of gravity, negates their strength while enhancing our own and renders their movement or attack futile.

The body is quite sensitive to this feeling of unbalance and will react swiftly to rectify itself, so any attempt to unbalance must be done swiftly and without notice. When we are pushed or grabbed our first instinct is to push and grab back. In many instances these reactions give our attackers bodies the information they need to readjust their center of gravity, their balance and remain strong. When we are punched, or attacked with a weapon, the way in which we try to block or try to stop the attack, telegraphs the same information and is counter productive to our defense.

The creation of unbalance and lose of center must be subtle and imperceptible to the attacker. Any attempt at readjustment once the movement begins must create pain and further unbalance and negate or absorb the attackers momentum. The movement should be over before it begins. The Kuzushi of an attacker can be felt by degrees within a circle or inches on the floor. To disrupt it requires an understanding of both motion and movement, what creates weakness and what creates strength, how to create an undisturbed line of force, position and posture which will allow you to counter balance an attack and apply your desired 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.

A Story Of the Butterfly

One of the main tenets of Buddhism revolves around the belief that everything and everyone in the universe is interconnected and interdependent one on another. This concept of “dependant arising” or dependant origin states that at every level of circumstance and existence there exists a “mutually interdependent web of cause and effect.” Since the creation of Buddhism two thousand years ago this philosophy has been debated and called by many different names by those outside the teachings of Buddha. Most recently, the concept of the six degrees of separation has become a popular concept in Western civilization to illustrate the same idea, that everthing and thus everyone is connected to everthing and everyone else.

Scientists today generally accept the principle of the “Lorenz Butterfly” which presents the idea that the simple flapping of a butterflies wings in one part of the world create tiny changes in the atmosphere which can change or alter, prevent or delay, speedup or slow down the path or even the occurance of a tornado in another part of the world. The idea that climate in one part of the world can affect the climate in another part of the world, that the hurricanes which effect the southern coast of the United States begin as tropical waves off the coast of Africa, or that pollution from cars and coal in the United States effect the degree and speed at which ice is melting in Anartica , has been gererally accepted throughout the world. Accepting this principle of “dependant arising” brings the more interesting question ,had the butterfly not flapped its wings or had not existed entirely, would there have been a tornado?

To put a more human face on this concept consider this story. A young man living with his parents just outside New York City, graduates college a gets his dream job on Wall Street. After some time learning the in’s and out’s of this new job he gets an opportunity to advance and is sponsored by his employer to takes additional classes which will allow him to take the tests for mandatory federal licences which in turn will allow him to further advance his career. He and those in class complete those courses, take and pass the the required exams . To celebrate the all go out for an evening on the town. He arrives home, to his parents house very, very, late that evening and as a result of lets say, to much fun, gets up late the following morning. So late that he misses his regular train. There is however in this town two train lines which will take you into New York City. He rushes to the other train, and arrives in NewYork only about 15 minutes later than he normally would. He is about three blocks away from his work but actually six blocks from where he would usually stop to pick up coffee and a bagel before he went to his office. So he looks around and finds a coffee shop and goes into buy his coffee and bagel. There is a young girl behind the counter, she fumbles with his order, its her first day on the job. She arrived just the day before from Brazil. This is her uncle’s coffese shop. The young man never goes back to his other coffee shop, nor does he ever take any other train into work. A little more than a year later they were married. I made her, her engagement ring and their wedding bands and over the thirty years that I have been manufacturing jewelry I have dozens of stories just like this.

There are, of course, similar stories in everyone’s experience, in everyone’s life. Take this one from the martial arts. There was a teenager sitting home on a Saturday afternoon. He’s in the living room with his parents and grandmother. She was there every Saturday. He was waiting for the ballgame to come on, but it was raining and as was the style in those days, when the ballgame got rained out the T.V. station substituted a movie. They were usually action movies , westerns or war films were very popular in those days usually with stars like John Wayne or Errol Fynn , Randolph Scott or Joel McCrea, in the lead roles. Many were still in black and white, not color like today. That was the case on that Saturday. An old James Cagney film named “Blood on the Sun” played that day. Set in Japan, just before WWII, it is a film filled with intrigue, espionage and plenty of action. The action is pure judo and jujutsu. Cagney as it turns out was a real judoka and did all his own stunts. The teenager was absolutely enthralled and mesmerized by what he saw on the T.V., so much so that he talked about the movie with his father for much of the following week. The boy’s father, looking for something to keep his teenage son interested in for more than ten minutes at a time, looked in the local yellow pages, found a martial arts school reasonably close to where they were living and one evening took his son to watch a judo class. The judo class was actually finishing when they arrived but the owner of the school allowed them to watch the next class, a class of jujutsu. The teenager joined that very evening and within a year was allowed, even though he was quite young at the time, to join the jujutsu class. Some forty five years later he is still as excited to be in thoses classes as he was as a fourteen year old boy.

I never actually had a chance to thank Mr Cagney for making that movie or for giving me my first glimpse of the martial arts. I suppose I could have though. A few years after my father retired, he bough a fifty acre apple farm in upstate New York. Mr Cagney was our neighbor. He owned the farm next to us, butterflies and all.

The Benefits of Martial Arts for Children's Mind, Body & Soul

It doesn’t take much these days to pick up some newspaper or magazine and read how we all are at increased risk for some terrible disease or chronic medical condition because of what we eat and drink, how we live and what we breathe. As a society it would not be hard to argue that many of these problems are of our own making. Our own excesses and that of societies have led to poorer nutrition, less exercise and more and more pollutants being put into our air and water. While these problems will pose great challenges for everyone in society, the children of our society have the greatest risks. Scientists tell us that childhood obesity is now at record levels. According to U.S. Governments Center for Disease Control “One-half the population below the age of 18 will be considered clinically overweight or obese by 2010”. Being obese puts children at a greater risk for high blood pressure, elevated cholesterol levels, diabetes, and asthma. New studies suggest that those who are obese face the further challenge of developing many of these other chronic conditions simultaneously. Later in their lives obesity and these other chronic conditions will lead to higher incidences of hypertension, heart disease, depression, and dementia. It will increase their risk for colon and ovarian cancer and reduce their life expectancy.

If this were not bad enough these health problems carry over to many other facets of a child’s life. Childhood obesity alone has been documented to reflect in a child’s feelings of isolation and poor self-esteem. While any of these health problems alone would be serious issues for any child to confront, these feelings of isolation and low self-esteem are also reflected in a child’s scholastic achievements as well as his/her social interactions with their peers.

However, many of the causes for obesity, diabetes and these other conditions are in our power to control, modify and change. Better nutrition and eating habits can be learned, focus, direction and exercise can be taught and a better, healthier lifestyle can be the result.

The martial arts have a long and deep history. They are filled with stories of bravery and loyalty, dedication and self-sacrifice. They are designed to motivate, to teach self-control, and perseverance. They incorporate a social system with 100-year-old traditions, which allow for individual growth and excellence. The health benefits of its exercise programs are enumerable, whereby the students gain not only the benefits from the exercises themselves but from practicing the skills they learn during each class. The martial arts are goal oriented and teach students focus and concentration in order to achieve their objectives. The relationships students develop with their instructors and fellow students further advance these skills and often carry over to many other facets of the student’s lives.

Today’s martial arts of judo, karate, aikido and jujutsu are ideally suited for the problems of to day’s youth. Teaching physical fitness, mental acuity, persistence, respect, and honor, the martial arts present responsible role models with a positive message for children of all ages. Students learn from a mentor or teacher not only the actual movements or techniques related to each individual art, but a series of life lessons related to their individual development and growth. Advancement is achieved through diligence and hard work, self-sacrifice and dedication.
This training enables the student to develop self-confidence and an acute understanding of their potential. Through the example of their teachers and fellow students new practitioners see not only what is, but also what could be. Their mental vision is enhanced and their imagination enlivened. Children who participate in these arts can be both inspired and awed. They learn about better nutrition and can develop better eating habits. The rigors of each art contribute to physical fitness and pride in each child. The lessons learned through the physical training of these arts teach children respect for themselves as well as others.

The martial arts through both its tradition and example, teach children about respect and dignity. It can instill in children a feeling of self worth and self-respect unequaled by any other activity. Finally, and perhaps most importantly it can make children unafraid, both physically and mentally, to visualize, grow, and confront the many challenges which they will encounter as they develop into adults.