The Axioms of Jiu-Jitsu

I have been observing something through the experiences of practitioners—a particular kind of knowledge that resists articulation, that lives in the body rather than the mind, and yet contains a logical structure as rigorous as any mathematical system.

The martial art known as Brazilian Jiu-Jitsu presents an interesting epistemological problem. There are hundreds of techniques, perhaps thousands. Guard passes, sweeps, submissions, escapes. New variations emerge constantly; old techniques are refined and combined. A practitioner could spend a lifetime memorizing moves and never reach the end.

And yet.

The masters do not think in terms of techniques. When they roll, they are not running through mental databases, selecting the appropriate response from a catalog of options. They are doing something else—operating from a deeper layer of understanding that makes the right move obvious when it remains invisible to their opponents.

This suggests that beneath the surface complexity lies a simpler structure. First principles. Axioms. The irreducible truths from which everything else derives.

What follows is my attempt to identify them.

The Mathematical Precedent

The approach has precedent in the history of knowledge.

In mathematics, axioms are statements accepted as true without proof. They are the foundation upon which everything else is built. Euclid constructed the entirety of geometry from five axioms—statements so simple they seem almost trivial. Two points determine a line. All right angles are equal. From these emerged triangles, circles, the Pythagorean theorem, and eventually the entire edifice of geometric knowledge.¹

The philosopher Aristotle recognized that all systematic knowledge requires such foundations:

"Every demonstrative science must start from indemonstrable principles; otherwise, the steps of demonstration would be endless." ²

What if jiu-jitsu worked the same way? What if there existed a small set of fundamental truths—principles about bodies, leverage, and control—that remained constant regardless of whether one was executing a kimura or an armbar, passing guard or escaping mount?

If those axioms could be identified, perhaps a practitioner could stop drowning in techniques and start understanding the art.

Axiom 1: Position Before Submission

This principle is so ubiquitous that it has become almost invisible. Every practitioner knows it. Few understand what it actually means.

The standard interpretation is strategic: "Get a good position, then attack." This is true but incomplete. The axiom is not merely advice about sequencing. It is a statement about the physics of control.

The biomechanist Stuart McGill, whose work on spinal mechanics has influenced martial arts training worldwide, explains the underlying principle:

"Force production requires a stable base. You cannot fire a cannon from a canoe. The body must be stabilized before it can generate or transfer force effectively." ³

A submission is an application of force to a joint or blood supply. That force must come from somewhere. If the attacker's position is unstable, the force will dissipate before it reaches the target. The defender will feel pressure but not the sharp, inescapable leverage that produces a tap.

This is why beginners hunting armbars from inside an opponent's guard fail repeatedly. They have reached the arm, but they have not controlled the body. The opponent can move, adjust, create angles that dissipate the attacking force. The technique is mechanically sound; the position is not.

Position before submission is not advice. It is physics.

The judoka Kyuzo Mifune, perhaps the greatest technician the art has ever produced, put it succinctly:

"Correct movement flows from correct position. Incorrect position makes correct movement impossible." ⁴

Axiom 2: Two Points of Control

This axiom emerged from observation of what works and what fails in the application of control.

A single grip is insufficient. One point of contact allows rotation around that point. The opponent can pivot, spin, create angles that nullify the grip's effectiveness. It is like trying to hold a door closed by pushing at a single point near the hinge—all the effort accomplishes nothing because the door can still swing.

Two points of contact create a line. And a line constrains rotation.

Consider the fundamental positions:

Mount: knees pressing on both sides of the opponent's hips
Side control: shoulder pressure on the face combined with hip control
Back control: seatbelt grip across the torso plus hooks inside the thighs

Each stable position has at least two anchor points. Remove one, and the position becomes precarious. The opponent can start to move, to create space, to escape.

The principle extends beyond positions to techniques themselves. The arm drag works because it involves two grips—one on the wrist pulling, one on the tricep pushing. The combination creates a rotational force that the opponent cannot resist with mere strength. A single grip could be countered by pulling away; the second grip makes pulling away ineffective.

This is why training partners who feel impossible to move always seem to have more grips than expected. They are not stronger. They are simply applying the axiom more rigorously.

Axiom 3: The Spine Dictates Everything

Here is an interesting way to conceptualize the human body: we are essentially tubes with appendages.

The spine is the central axis. The limbs are extensions of it, levers connected to a central structure. Control the spine—bend it, twist it, straighten it against the opponent's will—and you control the entire system.

Most submissions are simply creative ways to attack the spine or its extensions:

Chokes: compress the blood supply at the top of the spine (the neck)
Armbars: hyperextend a limb away from the spine
Back control: curl the opponent into a ball, folding the spine against itself
Leg locks: attack the joints furthest from the spinal axis, where the opponent has least control

The physiologist Thomas Myers, whose work on fascial connectivity has influenced movement science, describes the body as a "tensegrity structure"—a network of tension and compression elements that work as a unified system.⁵ Stress applied anywhere in the system propagates throughout. The spine is the central element that organizes the entire structure.

This explains why good grapplers seem to control everything at once. They are not actually controlling the arms and the head and the hips separately. They are controlling the spine, and everything else follows.

It also explains the power of frames and postures. When the spine is properly aligned, the body can resist enormous force. Break the alignment—kyphotic curve in mount, twisted spine in side control—and the body collapses under its own weight.

Axiom 4: Create Dilemmas, Not Moves

This may be the most important axiom, and the one that separates advanced practitioners from beginners.

A single attack can always be defended. Always. The number of defensive options for any given technique is large, and a competent opponent will find one. Throwing isolated techniques is playing a slot machine, hoping the opponent does not know the counter.

The goal is not to execute a perfect technique. It is to create a situation where defending one threat exposes another.

The game theorist John von Neumann formalized this insight in his work on zero-sum games. In any competitive situation, pure strategies—doing the same thing every time—can be exploited by an opponent who identifies the pattern. Optimal play requires mixed strategies that force the opponent into genuinely difficult choices.⁶

In jiu-jitsu terms: attack the arm. The opponent defends. Now their neck is open. Attack the neck. They defend. Now the arm returns. Loop the sequence until something breaks.

The greatest practitioners never present problems with single answers. They create systems of interlocking threats where each defense opens a new vulnerability. The opponent is not beaten by a technique; they are beaten by the logic of the situation, where no available choice is good.

This principle appears in chess under the concept of "zugzwang"—a position where any move makes the situation worse. The jiu-jitsu equivalent is a dilemma so tight that every defensive action improves the attacker's position.

Axiom 5: Efficiency Over Athleticism

Jiu-jitsu was explicitly designed for the smaller, weaker person to defeat the larger, stronger one. The Gracies developed their art in Brazil, constantly testing it against larger opponents in challenge matches. The premise of the art—its founding bet—is that technique trumps attributes.

This promise only materializes if efficiency governs every action.

Efficiency in this context means maximum effect for minimum energy expenditure. The physicist would call it mechanical advantage—using leverage, angles, and timing to multiply force rather than relying on raw strength.

The judoka Jigoro Kano, founder of judo and an early theorist of grappling mechanics, articulated the principle he called "seiryoku zenyo"—maximum efficiency with minimum effort:

"Whatever be the object, the best way of attaining it shall be the use of mind and body in the most efficient manner... The principle of maximum efficiency demands that we should use our physical and mental energy in the most effective manner." ⁷

When a technique feels hard—when it requires muscling through resistance—something is wrong. Either the timing is off, the angle is incorrect, or a precondition has not been established. The right technique, properly applied, should feel almost effortless.

This does not mean strength is irrelevant. Two practitioners of equal technique, the stronger one wins. But technique has a multiplicative relationship with strength. Double your strength and you double your effectiveness. Double the efficiency of your technique and you might increase your effectiveness tenfold, because you are now accessing leverage ratios that were previously unavailable.

The tell for efficiency is sustainability. Explosive techniques that require maximum effort might work in round one. By round six, when exhaustion has degraded physical capacity, only efficient technique remains.

The Recursion Problem

I must note an incompleteness in this analysis.

These axioms may not be fully independent. Position before submission might derive from the two points of control axiom—good position being defined as the establishment of sufficient control points. The spine axiom might be a corollary of the physics underlying all positional control. Perhaps there are only three fundamental principles, or perhaps there are ten.

The philosopher W.V.O. Quine argued that all our knowledge forms an interconnected web, where no individual belief can be verified in isolation from the others.⁸ The same may apply to jiu-jitsu principles. They form a system, and the system only makes sense as a whole.

This is not a failure of the analysis. It is a recognition that martial arts, like other forms of embodied knowledge, resist the neat separability that formal systems prefer. The art is a unity. The axioms are not separate truths but different angles on the same underlying structure.

The Philosophical Dimension

There is something deeper here than sport or self-defense.

The martial arts have always served as laboratories for exploring questions about mind and body, knowledge and action, the relationship between thinking and doing. The phenomenologist Maurice Merleau-Ponty argued that the body possesses its own form of intelligence—a "motor intentionality" that cannot be reduced to conscious thought:

"The body is our general medium for having a world. Sometimes it is restricted to the actions necessary for the conservation of life, and accordingly it posits around us a biological world; at other times, elaborating upon these primary actions and moving from their literal to a figurative meaning, it manifests through them a core of new significance." ⁹

Jiu-jitsu develops this bodily intelligence in extreme form. The practitioner acquires a feel for leverage, for timing, for the moment when resistance becomes opportunity. This knowledge lives in the muscles and the nervous system. It cannot be fully captured in words, yet it is not therefore irrational or mystical. It is simply a different mode of knowing.

The search for axioms is not an attempt to reduce this embodied knowledge to abstract propositions. It is an attempt to find the bridge between thinking and doing—to identify the principles that connect the realm of articulate understanding to the realm of bodily skill.

The Ongoing Inquiry

I do not claim this analysis is complete. New training, new observations, new practitioners may reveal axioms I have not identified or demonstrate that my current formulations are imprecise.

But the method feels sound. When learning a new technique, ask which axioms it expresses. When a technique fails, ask which axiom was violated. When watching a master roll, look for the axioms they embody more fluently than their opponents.

The purple belt who crushes the blue belt is not running through a larger database of techniques. He is expressing the axioms more purely. He does not think about position before submission; he cannot imagine any other way to operate. The axioms have become invisible to him because they have become part of his body's default programming.

That is the goal. Not to memorize a thousand moves, but to understand the handful of truths they all express. To let the axioms sink so deep that technique emerges spontaneously, like mathematics emerging from axioms, like geometry emerging from points and lines.

The gentle art yields its secrets slowly. But it yields them to those who ask the right questions.

Bibliography

Heath, Thomas L., ed. The Thirteen Books of Euclid's Elements. Cambridge University Press, 1908. ↩
Aristotle. Posterior Analytics. Translated by G.R.G. Mure. The Internet Classics Archive, Book I, Part 3. ↩
McGill, Stuart. Ultimate Back Fitness and Performance. Backfitpro Inc., 2004, p. 67. ↩
Mifune, Kyuzo. The Canon of Judo: Classic Teachings on Principles and Techniques. Kodansha International, 2004, p. 33. ↩
Myers, Thomas W. Anatomy Trains: Myofascial Meridians for Manual and Movement Therapists. Churchill Livingstone, 2001. ↩
Von Neumann, John, and Oskar Morgenstern. Theory of Games and Economic Behavior. Princeton University Press, 1944. ↩
Kano, Jigoro. Kodokan Judo. Kodansha International, 1986, p. 21. ↩
Quine, W.V.O. "Two Dogmas of Empiricism." The Philosophical Review 60, no. 1 (1951): 20-43. ↩
Merleau-Ponty, Maurice. Phenomenology of Perception. Translated by Colin Smith. Routledge, 1962, p. 146. ↩