A geodesic is a straight line on a curved surface. A centripetal geodesic is one which leads to a central point. For a martial artist, this central point is usually the centre of the body or the centre of the earth.
A martial artists develops power by creating a path of maximum tensile modulus through the body, and manipulating that tensile geodesic using the whole body in ways that maximize mechanical efficiency. If parts of the upper body move independently and without regard for maintaining the centripetal geodesic, then the mechanical efficiency is lost.
For example, if the arms are in an ideal structure that connects the opponent’s force to the ground through the path of maximum tensile modulus, they will employ several class 3 levers that disrupt the power of the body.
The centripetal geodesic must be adaptive, meaning that the path of maximum tensile modulus is not static, and adapts in shape, length and volume in order to compensate for changes in the relationship between the martial artist and the opponent/s.
The centripetal geodesic relies not only on the high tensile modulus, but also on the low shear modulus, meaning that there should be little to no lateral resistance to the opponent’s pressure.
Physical or mental attachment to a particular shape of a centripetal geodesic negates the whole point of it. The geodesic must be fluid, adaptive, and independent of physical reference frames.
A martial artist maximizes effectiveness and efficiency by directing forces and momentum along geodesics relative to central frames of reference.
These geodesics can be manipulated consciously or unconsciously, and can change one’s own frame of reference or the frame of reference of the opponent.
Attachment to reference frames or the interacting geodesics is the lead cause of defeat in combat.
Success in combat is determined by the adaptability of the martial artist to adapt to changing geodesics and to avoid attachment to any particular reference frame.
Typically, the frames of reference in martial arts are:
- centres of gravity (within combatants, or their weapons, or the Earth)
- centres of rotation
- centres of mental or emotional attention
A geodesic is a straight line in curved spacetime, or on a curved surface.
The body and mind can create shapes that connect forces and frames of reference both instantly and over time. When those shapes are curved appropriately, they can result in mechanical, tactical, and strategic advantages.
Learning to create geodesic sets in the body and mind can manipulate not only the forces and momentum within various reference frames, but change the reference frames themselves.
Frames of Reference:
A frame of reference, or reference frame, is the set of coordinates by which one thing is measured against another.
If you are walking on the roof of a train that is winding through mountainous terrain, your balance is dependent on your position relative to the train. It serves you well to measure your position and momentum relative to the train.
Intersecting Reference Frames
Interactions between entities involves the interaction of various frames of reference. As these frames interact, they affect the relative direction of force, momentum, and consciousness.
If you continue walking along the roof of the train, but focus on the mountains or a passing object that is going in a different direction, you will walk off the train whenever there is a significant bend in the tracks.
Likewise, your opponent’s nose and the ground beneath your feet might both be coordinates in your frame of reference when you throw a punch at their nose. But if they intercept your fist and/or your attention with a hand or a distraction, then either their nose or the ground (or both) may suddenly cease to be part of your frame of reference.
Such interceptions are most effective when they are gradual enough for the relative velocities and/or forces involved but significant enough to affect their relationship to at least one frame of reference.
Too sharp a curve or too little, will not prevent the fist from hitting the nose.
A well chosen set of geodesics will cause the opponent to defeat themselves, or even prevent the frames of reference from interacting in any obvious way.
Events vs Things:
What we often think of as objects, forces, or energy, can be more accurately described as events that occur when frames of reference interact, such as the interaction between mass and spacetime. Gravity is an event that occurs when a mass interacts with spacetime. Energy is an event that occurs when yin and yang interact. Learning to think of things this way can greatly improve your interactions, and make you a better martial artist.
Internal martial artists often speak of chi (qi) and energy, and internal power, in ways that help students to feel how they should interact with other reference frames, such as that of an opponent. But qi is not a thing. It is an event that occurs when frames of reference, such as mind and body interact. (Note that mind and body can be one thing, and also exist as different frames of reference.)
Geodesics, Chi (qi), and the 8 postures of tai chi:
“Internal energy” is the traditional way of describing the ways in which geodesics can be used to manipulate frames of reference. In tai chi, the most fundamental expressions of power are categorized using the analogy of the 8 trigrams, (heaven, earth, water, fire, thunder, mountain, lake, wind). In practice these apply to 8 types of geodesic arrangements that can be used to defend oneself and disrupt the opponent.
The energies can refer to the way that geodesics are arranged within one’s own body.
Attention to the outside of your forearm feels like energizing “peng jing” (boing power), and sets up centripetal geodesics that will connect an opponent’s force to the ground beneath your feet. Attention to the palm of the hand will energize “Lu jing” (rolling quality) and sets up different sets of geodesics suitable for putting an opponent’s force into orbit around your centre or a common barycentre. Focusing on the insides of the forearms sets up geodesics for “Ji” (cramming), and focusing on the small of the back sets up geodesics for “An” (press). Alternating lateral pulses can move the opponent sideways (Lieh). Moving energy up and down can make the opponent float (Zai). Folding energy can penetrate their defences with an elbow or knee (Zhou). Condensing qi can convert angular momentum into a powerful strike with the hips, shoulder or trunk.
The 8 postures can also refer to the way in which you can manipulate the geodesics within the opponent’s body. So, the opponent can be made to bounce, roll, obsess, sink, float, stumble, fold, or lean.
In martial arts, it is useful to think of geodesics and geodesic sets changing instantaneously, without any time required to transfer between them. A line does not move. You just alter your frame of reference to engage the opponent with another geodesic set. In one instant, you “feel the qi” on your forearm. The next instant, you “feel the qi” in your palm. There is no movement of the sensation from one place to the other. It simply switches. (Does anyone know if there might be a Lagrangian or Hamiltonian formula for this? 😉 – Ian)
The fundamental flaw in human nature, which leads to defeat in combat, is the untimely attachment to a particular frame of reference. The universe changes, and the mind is still looking at what it was.
Example: To throw a punch, you frame yourself between the ground and your fist, and the opponent’s nose. Your mind sees/feels/imagines the impact of fist with nose, and is still imagining it after the opponent moves the nose out of the way and aligns their punch with your ribs.
In that moment, you are still attached to the universe where your punch hit their nose. But their nose is in a universe where you are about to find it very difficult to breathe.
The Zen monk, Takuan Sōhō (1573 CE– 1645 CE), called the reference frame where the mind became attached, “The abiding place” and warned against the affliction of “abiding in ignorance.”
“…To speak in terms of your own martial art, when you first notice the sword that is moving to strike you, if you think of meeting that sword just as it is, your mind will stop at the sword in just that position, your own movements will be undone, and you will be cut down by your opponent. This is what stopping means.
Although you see the sword that moves to strike you, if your mind is not detained by it and you meet the rhythm of the advancing sword; if you do not think of striking your opponent and no thoughts or judgments remain; if the instant you see the swinging sword your mind is not the least bit detained and you move straight in and wrench the sword away from him; the sword that was going to cut you down will become your own, and, contrarily, will be the sword that cuts down your opponent.
In Zen, this is called ‘Grabbing the spear and, contrariwise, piercing the man who had come to pierce you.’ The spear is a weapon. The heart of this is that the sword you wrest from your adversary becomes the sword that cuts him down. This is what you, in your style, call ‘No-Sword.’
Whether by the strike of the enemy or your own thrust, whether by the man who strikes or the sword that strikes, whether by position or rhythm, if your mind is diverted in any way, your actions will falter, and this can mean that you will be cut down.
If you place yourself before your opponent, your mind will be taken by him. You should not place your mind within yourself. Bracing the mind in the body is something done only at the inception of training, when one is a beginner.
The mind can be taken by the sword. If you put your mind in the rhythm of the contest, your mind can be taken by that as well. If you place your mind in your own sword, your mind can be taken by your own sword. Your mind stopping at any of these places, you become an empty shell….”
From Takuan’s letter to Yagū Munenori, called “The Mysterious Record of Immoveable Wisdom”. (Translation by William Scott Wilson in his book, “The Unfettered Mind” ©1986
The immoveable mind is one which does not identify with a frame of reference. It is like Wuji, the non-dualistic state that encompasses duality without being a part of it. Duality is like “Taiji”, the interaction of yin and yang. From the perspective of Taiji, Wuji is a separate state of existence. But from the perspective of Wuji, there is no distinction between Wuji and Taiji.
We don’t tend to talk about the frameless reference because, well, we can’t. As Laozi said, “I know you believe that you understand what you think that I said. But I’m certain that you don’t realize that what you heard is not what I meant. The Dao that can be spoken of is not the Eternal Dao.”« Back to Glossary Index