The shortest distance between two points is zero. But let’s talk about geodesics. More specifically, let’s talk about what I call the centripetal geodesic. It is the key to Peng, and internal power. It is also at the core of all advance martial art strategy and tactics.
Here is a beautiful video explaining geodesics.
This is the transcript for my video, Introduction to Tai chi, Episode 15
For a long time, martial arts jargon has included concepts of hard styles, soft styles, internal styles, external styles, and people have conflated those things with ideas of internal power and external power. Each of these concepts is a big deal, especially in some lineages, and they have been the subject of pedagogy, marketing, and kungfu politics for decades. Martial artists have been known to literally fight over the meaning of these terms.
In this video I’m going to talk about how all of these concepts are related to a particular fundamental principle that is found in all martial arts.
This principle has been taught in many different ways, using different types of terminology. Like a lot of the terminology that is used in martial arts, I have found most of it to be potentially misleading, incomplete, idiomatic, confusing, convoluted, or simply not specific enough.
I call it the centripetal geodesic principle.
Depending on the depth or breadth of your experience, you might recognize it under other terms. But these terms often combine this concept with other things, which is easy to do because it is related to everything else about martial arts.
But bear with me, because I’ve put a lot of thought into deconstructing this, and I think it makes it much easier to teach martial arts if students understand this principle. I believe that the centripetal geodesic principle can allow students of different martial arts to talk about what they do in a way that makes sense to people of other lineages without having to translate everything into ancient Chinese.
This might be a new way of looking at it, and it might not make much sense at first. But hang in there.
How you use this principle will affect your coordination, agility, balance, awareness, strength, breathing, relaxation and more. It will help determine a martial artist’s skill level, strength, power, tactics, strategy, timing, accuracy, sensitivity, responsiveness and speed.
Failing to apply this principle is to rely on what some people call external power.
To apply this principle correctly is to involve core strength to generate power more efficiently. This is what some people call internal power, and others just call whole body power, or good leverage.
Applying this principle very well is to use subtle strength to generate power accurately, like pushing a needle with rope. This what some other people call internal power.
One of the highest uses of this principle is to manipulate frames of reference in a way that can cause the opponent push themsleves with a rope, which is what some people mean when they refer to ”internal martial arts”, or what other martial arts call, “being really really good at martial arts.”
Centripetal Geodesic is two words. The first is Centripetal.
Centripetal means “toward the centre.” In this case it can refer to a person’s centre of gravity, a centre of rotation, or the centre of the earth. Centripetal acceration, for instance, is acceleration toward the centre of something. It is what you feel when you drive around a sharp curve. If you accelerate straight forward in a sports car, you feel yourself pressed against the car seat as it accelerates you forward. When you achieve a constant cruising speed, that pressure stops. When you go around a corner, you feel the side of the car push you toward the center of the circle. That pressure stops when you straighten out. When you swing a pail full of water around, you can sometimes feel the resistance of the water as the bottom of the pail pushes the water toward the centre of the circle. (That resistance is what we call centrifugal force, which isn’t really a thing. It’s just the inertia of the water trying to keep going at a constant speed in one direction while you keep accelerating it toward the centre. Centrifugal force would be like the force you apply to the seat when the car accelerates forward. You are not applying force to the seat. The seat is applying force to you.)
If someone were to throw you to the ground and stand on you, you feel the pressure as they accelerate you, or a part of you, toward the centre of the earth. You will also feel the earth resisting that acceleration. If the surface of the earth were not there, then you would not feel the pressure because there would be no relative change within that frame of reference. The opponent would be moving the same speed as you, just as you would feel weightless in your car if your car went off a cliff.
That is why an astronaut in orbit does not feel any G-force from the acceleration, even though the orbiting space ship is constantly accelerating toward the centre of the earth. The reason they don’t crash into the earth is that they are very good at missing it. As Douglas Adams wrote, “All you have to do to fly is throw yourself at the ground, and miss.” The satellite is moving laterally (or sometimes longitudinally) just fast enough to avoid hitting the earth, even as it accelerates towards it. That’s right, you can move at a constant speed and still be accelerating, because the direction is constantly changing.
So, “centripetal” means “toward the centre”
What is a geodesic.
A geodesic can be thought of as a straight line on a curved surface, or in curved spacetime, or in a curved frame of reference. If you get in a plane and fly in a straight line for long enough, you end up on the other side of the planet. So, you went straight. But the medium you went through was curved.
In Euclidean geometry, a straight line is the shortest distance between tow points. Bruce Lee said that simplicity is the shortest distance between two points. A straight line between antipodes would go straight through the centre of the Earth. But that is not the simplest way. It is much simpler to follow the geodesic all the way around the earth than to drill through it.
But where gravity and spacetime are concerned, the shortest distance between two points is a geodesic. But curved surfaces are not always spherical, so, while the shortest distance is always a geodesic, not all geodesics are the shortest distance between two points, except when… okay never mind, that’s another story.
Now, I always say that, in martial arts, the shortest distance between two points is always zero, which means there is only one point, which is the point. The goal is to have already achieved the goal. Hence the instruction from famous martial artists like, “There is no enemy” or “Start the fight by winning” or “Don’t move” or “Don’t do anything”, to which the student says, “Yeah, well, how do you do that?”
Then the teachers says, “No. You don’t.”
Another way to think of it is to connect the opponent to the target so that they have no where to go except anywhere else besides the target. That is where the centripetal geodesic comes in with intersecting frames of reference, and trying to make your opponent divide their attack by zero, so it becomes undefined. But that stuff is over my head. So, let’s back up a bit.
Lets look at this slightly faded belt. If you are a tiny myopic creature walking along the surface in a straight line, you won’t notice if the surface is curved. The surface is your frame of reference, and you just keep going. Of course, if you go very fast and the curve is too sharp, you will go off the road, or into space. If you go slowly enough, or the curve is gradual enough, you will stay on the road and not notice that it is curved.
Gravity is what happens when mass does that to spacetime. Gravity is the weakest force in the universe. But if there is a planet worth of mass, it can twist and compress the frame of reference (spacetime) so that something that tries to move past it will find itself moving towards it. It still thinks it is going in a straight line, just like that airplane. But the spacetime itself is curved. And since spacetime is compressed, it will move faster as it gets closer. It hasn’t tried to speed up, the distance has shrunk.
If a friend is walking parallel to you, and you both walk straight forward you might expect them to stay beside you. But if the surface is curved, then straight forward is different for them than it is for you. A slight difference in starting positions might take you very different directions. If you were walking along this belt, you might find yourselves on opposite sides of the belt, as if you were in parallel universes.
In combat, this can mean the difference between being in a universe where you get punched in the nose, and a universe where the punch misses you completely, even though you haven’t moved.
In general combat, as with General Relativity and with solo martial arts practice, we are constantly negotiating with gravity. But try not to think of gravity as a thing, or a force. Consider what we thing of as gravitational forces, as actually being events that happens when frames of reference interact. I guess that gravity and consciousness are very similar in that sense.
Solo practice is when we learn to direct the forces of gravity through the body along gentle curves. You try to align the different parts of the body like a string of pearls or a guitar string, balance on end. We teach ourselves to let gravity flows through us along geodesics that minimize erratic accelerations. We don’t want the corners to be so sharp that gravity goes off the road. We don’t slouch or stand crookedly. We stand in a way that keeps all the geodesics aligned with the fascia and bone. We want to align with stress and reduce strain.
Typical human posture can be tense and chaotic. There is a tendency toward disorder, with vectors of force going off in all sorts of tangents. One day, a student of mine, an engineer, said, when asked how she was doing, “Entropy is winning.”
Good Tai chi posture resists entropy and strain. It is both plastic and elastic, and minimizes stress by keeping those geodesics pointed at the centre of the earth. In solo practice, you are aligning geodesics with your own weight.
In combat, you are also connecting those geodesics with the opponent’s force, leading it through your body and into the centre of the earth, or diffusing it through your own body to minimize damage.
You can also redirect the opponent’s force away from your body while staying connected to your opponent’s centre. That way, they are never on target, and you are always on target.
Look at this guitar string. If I push two points together, the string folds in n-y number of ways. The vectors of force go between my hands and don’t pass through the string, and I can bring my hands together. But if the string is perfectly aligned, and I push in exactly the right directions, then the string transmits the force between the hands and does not collapse. My hands will therefore not meet. The longer the string is, the more this depends on extraordinary precision.
I could also use a shorter section of the string, so that the coils in the guitar string preserve the structure. This way, even if I am not very precise with the angle of my push, the string can preserve its structure, and the force gets redirected along the curve, and my hands do not come together
The ability of external forces to collapse the arc is dependent on a few factor, like the material of the string, the structure of the coils, the density of coils per arc length, the amount of the force, the angle of attack, etc.
The thing is that the arc either collapses or it doesn’t, or something else happens.
If someone pushes on my forearm, it might collapse, and they could strike my body or face. But if I can align my arm in the right way then the force is transmitted through my arm into my centre. The arm does not collapse, and they cannot hit the target. The same alignment will be useful if I strike a target. The whole body’s power can be expressed through the arm into the target if everything is properly aligned. If the alignment is not precise enough, it can still work so long as my arm is strong enough to fight the deformation, (and prevent spraining my wrist, for instance). In martial arts, the fascia is aligned, and the muscle supports the fascia. The more perfectly the fascia is aligned, the less muscle is required. The worse the alignment, the more muscle is needed. Proper alignment stabilized by muscle is what allows us to avoid what I call ”class-three-lever syndrome”. Bad alignment makes stabilization difficult or impossible, and prevents the body power from reaching the target.
When the alignment is perfect, then we have a mechanical advantage over the opponent.
In tai chi partner exercises like tuishou (pushing hands) and with grappling and sparring, we learn to align the body in a way which uses centripetal geodesics to instantly connects opponent’s force to the ground. If they push us or pull us, we direct their force through our body into the ground, so that they are not so much fighting us as they are fighting the ground. (The thing about ground fighting is that the ground has amazing endurance.) If the geodesic goes outside body, then we end up using class three levers, and get pulled off our base of support.
Understanding the centripetal geodesic is what allows us to:
- use core power,
- use whole body power
- reduce our dependence on local muscle strength
- reduces or eliminates the use of class three levers.
- enables class 1 and 2 levers, wedges, wheels, Galilean cannons, and other simple machines.
- enables us to remain agile, balanced, flexible, and adaptable, even as we engage the opponent’s attack.
- reduces the chance of falling and decreases the chance of injury if we do fall.
But while building and reinforcing the structure that shapes the centripetal geodesic is an important part of most martial arts, higher level skill involves softening and narrowing that structure, refining the alignment and making the arc more and more adaptable, so it can shorten, length, move and instantly reposition itself without the need for vector translation.
One part of martial art training is strengthening the core muscles, and strengthening the connection of the extremities to the core. But there are differences in how it can be used. If applying this power requires the muscles to be tense, then this is not a good thing. Tension makes it more difficult to avoid the “class-three-lever syndrome“. More importantly, the use of muscular strength increases the number of paths that force can take through your body. It makes it possible for the opponent to manipulate you in many different directions.
True internal power minimizes the number of ways in which the opponent can manipulate you. Ideally, you will choose the options that you want the opponent to have, and you can change those in a way that allows you to remain relaxed, balanced, and agile.
If they are right on target, their force is transmitted along the centripetal geodesic, and they bounce off. If they are not on target, they go off the road and are not a threat.
You can use the centripetal geodesic to manipulate frames of reference. The opponent tries to push in one direction, and ends up pushing in another. They might start out focusing on you nose as a target, and end up focusing on emptiness.
In solo practice, we focus on the geodesics within our own mind and body. We make them broader and thinner, longer and shorter, and vary the shape of the arc. We learn to change them instantly from one shape to another without any vector transition.
I wish I had studied Lagrangian mechanics.
Your potential energy and kinetic energy can seem to superposition themselves, from the opponent’s perspective. (You can do that by mentally switching a fulcrum to a different part of the body. That’s another lesson. People do that in shuaijiao, judo, qinna, tuishou, and fencing… and boxing.)
But after we spend enough time manipulating the geodesics within our own body, we learn to manipulate the geodesics in the opponent’s body…and mind. We can seem to manipulate the size and shape of spacetime by intercepting their intent. We can shorten or redirect their punch by messing with their nervous system or point of view.
Many martial art schools begin by teaching the student how to punch and how to block a punch. Over time, we learn that blocking is a real waste of time. We also learn that a punch is not as linear as we thought. We learn that making assumptions about a frame of reference. When we assume a frame of reference we make a ref out of our ass.
When there is a fight, egos are like planets interacting with spacetime, twisting and shrinking frames of reference and causing matter to go in unexpected but somewhat predictable directions.
Novice students move within a simple frame of reference, using class three levers and too much muscle.
Intermediate students use whole body power and learn to integrate the core strength with the extremities. They develop multiple geodesics and are able to engage force from many different directions. But they tend to be tense, and engage many different directions at once. This enables them to resist in all directions, but makes them less agile, and allows the opponent to engage them in many more directions. The image that is sometimes used is “Bulls butting heads.” Intermediate students do that even when they are alone.
Advanced students refine the geodesics, using less force, less movement and less time. They engage the opponent with no more than one to four geodesics at once. They manipulate frames of reference to achieve their goal without force.
Mastery sees the liberation from any particular frame of reference. Their mind is immoveable, because there is nothing to compare it to. There is no fight. Yin and yang combine. They see the duality but are not attached to it.
Martial arts talk about hard styles and soft styles. Hard styles are supposed to be more linear and rigid than soft styles. But I’ve seen so-called hard styles be softer than soft stylists. At the higher levels, there is not much difference. Some schools produce better students. But that is not really about the style.
You will also hear people talk about internal power and external power as if they are stylistic differences. But it is really about skill levels. We should also not confuse internal power with internal martial arts. Sure, internal martial arts talk about internal power. But so do all other martial arts.
Internal power contains external power, but external power does not contain internal power. This means that the subtle and profound are built on the plain and superficial. “Internal Styles” is a term that martial artists gave to themselves. There was no such thing as an external style. That is a category that came later, as an insult.
A warning that one of my teachers gave us was, if you, as an internal stylist, go to a so-called external school where they have skilled students, like a good Shaolin school, or a good karate school, be careful what you say. He warned us, “If you say, ‘We do internal martial arts, with internal power. You do external martial arts, with external power. Internal power contains external power. But external power does not contain internal power. We are better than you.” He paused thoughtfully, and smiled. ”If you say that, I think maybe they will kill you.”
All styles can teach internal power. How they do it will be different.
It is said that jazz demonstrates the pinnacle of musical achievement, and that jazz is the Western answer to Zen. It is said that any musician who improves constantly, will eventually be playing jazz. This does not mean that great classical musicians cannot play jazz, or that studying at a jazz school will make you a great jazz musician.
Mastery is about learning the rules so well that you can break them.
The centripetal geodesic principle is a guideline that applies to all martial arts. It is not unique to what I do, or to tai chi, or to internal martial arts. Mastering it is a means to transcending it. Then it will be your style.
For a long time, martial arts jargon has includes concepts of hard styles, soft styles, internal styles, external styles, internal power and external power. Each of these concepts is a big deal, especially in some lineages, and have been the subject of pedagogy, marketing, and kungfu politics for decades.