The Maths of Aikido
Maths has become cool in the last few years. And mathematicians have become stars. There was Will Hunting in Good Will Hunting. John Nash in A Beautiful Mind. Alan Turing in Breaking the Code. And the natural maths genius Lisbeth Salander in the Millenium trilogy by Stieg Larsson. Maths would have been a lot more fun at school if they had shown us episodes of Numb3rs.The only thing that makes me truly happy is mathematics. Snow, ice, and numbers.
We use geometry concepts everywhere in aikido. One point. Lines. Space. Planes. Curves. Vectors. Spheres. Spirals.
The triangle, the circle and the square are sometimes used as basic aikido symbols. They can have different meanings and there are a few suggestions in the links below. The idea of a square is not very useful in practical applications. But the triangle and the circle are very useful concepts.
There is an interesting judo textbook called The Secrets of Judo by Jiichi Watanabe and Lindy Avakian. It is unusual because it uses maths and physics to explain judo throws and holds. The parallelogram of forces, moment, the coefficient of friction…
There is more than a page of equations just about how to fall - ukemi. Time and velocity and acceleration and mass and distance. And the resisting force of the mat.
It's a good approach. As long as you also do the physical practice. Just look at the words. Physics. Physical practice.
It is not difficult to teach a judo throw by numbers. In uchikomi or nagekomi practice with a partner if you step in a certain way, move your body in a certain way and break the balance in a certain way finally you can do a technically accurate judo throw. It takes a long time to learn a throw well enough to be used against an opponent who is also trying to throw. But if you have explained it clearly a white belt can execute an effective throw.
Aikido is perhaps a little different. You can also explain an aikido technique and demonstrate it and break it down by numbers. But however clearly and well you explain an aikido throw to a white belt and however well the throw is done the result will still look like a throw by a white belt.
Jigoro Kano the founder of judo himself used a simple maths model to explain the principle of judo.
Mathematics in the movies
Mathematics and Art
The Twilight Samurai | Tasogare Seibei
Abacus and Sword | Bushi No Kakeibo
photo: Grand Challenge Equations by Duncan Hull
my blog on aikiweb | my blog on wordpress
© niall matthews 2012
Niall Matthews lives with his family in Japan. He teaches aikibudo and community self-defence courses and has taught budo for twenty-five years. He was the senior deshi of Kinjo Asoh Sensei, 7 dan Aikikai. He was the exclusive uke of Sadateru Arikawa Sensei, 9 dan Aikikai, at the hombu dojo in Tokyo for thirteen years until Arikawa Sensei's death in 2003. He has trained in several other martial arts to complement his aikido training, including judo (he has 4 dan from the Kodokan in Tokyo), kenjutsu (for about ten years) and karate (for about three years). He originally went to Japan as a staff member of the EU almost thirty years ago. He received 5 dan from Arikawa Sensei in 1995. This 5 dan is the last aikido dan he will receive in his life. His dojo is called Aikibudo Kokkijuku 合気武道克輝塾. Arikawa Sensei personally gave him the character for ki in kokki. It is the same character as teru in Sadateru - not the normal spelling of kokki 克己. It means you make your life shining and clear yourself.
Re: The Maths of Aikido
Some aikido principles can be explained by physics. As an example, ALL techniques can be classified into one of the 3 simple levers. The lever has 3 components: the resistance, the force and fulcrum. The resistance is always the hara/center/dantien while the location of the fulcrum and force depends on the technique. The objective therefore is how to unbalance the resistance using any technique. This principle applies to all joints on a micro to macro level: micro for example are the fingers, thumbs (eg aiki age, aiki sage) macro being shoulder, elbow, neck (eg kihon waza).
Another example is the concept of non-resistance. This can be explained by the simple physics concept of work. The physics definition of work = Force X displacement X cos (angle). This is different from a layman's concept of work. The application to aikido is the force = line of KI and displacement is where you want uke/uke's body part to move. You are doing 0 work if the angle between uke's KI (line of force/movement) and where he's going is 90 degrees since cos(90) = 0. By doing 0 work, you are therefore using 0/minimal energy and also no power. This principle also applies on a micro/macro level and in all techniques.
Kuzushi is basically maximizing the effect of gravity in uke by tilting him from a perfectly upright position. A few degrees difference from the 90 degree position has a lot of effect from gravity.
By applying these physics concepts, you are literally integrating the "universe" within you since everybody succumbs to the physical laws. Nobody is immune. Imho, in aikido uke always has 2 opponents therefore will always be at a disadvantage: nage and the natural laws. Nage is just the "facilitator" applying the laws. IMO, in aikido nage's contribution is just a very tiny part in a perfect technique since it is the natural laws that uke succumbs to and not nage. Understand the natural laws and you will start understanding what aikido is IMHO. Aikido to me is basically applied physics in martial arts :-).
Re: The Maths of Aikido
A more recent math hero is Nate Silver ( http://en.wikipedia.org/wiki/Nate_Silver ) of FiveThirtyEight fame.
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