Invariants

The most important aspects of a technique are the ones that never change.

Do you sometimes struggle to learn new techniques? Do you have trouble remembering all the steps? Do you find that even when you do remember the steps, you can't make the move work against a resisting opponent?

I'm guessing your answer to each of these questions was “yes,” and that's no surprise because these problems are a natural part of the learning process. Everyone experiences these challenges in Jiu-Jitsu until they learn to loosen up a bit and get more flexible with their thinking. So let's talk about how to do that.

Jiu-Jitsu gets a lot easier to learn when you realize that some of the details you're being taught are more important than others. And focusing on those most important details will yield the biggest returns.

To understand how this works, let's first talk about invariants.

WTF is an “invariant?”

Don't worry, “Invariants” is not the name of a new Marvel movie. 🤣

An invariant is an aspect of the game that remains mostly constant, even when everything else is changing.

In a sport as complicated and chaotic as Jiu-Jitsu, it helps to know which things will hold constant.

Let me give you an example. When someone is standing in my guard, I can never truly know what they're going to do. They might try to stack me, or knee slice me...heck, they might even try to cartwheel over my head!

But regardless of their plans, I know one thing for certain: If I can make them bend their torso forward so their body is shaped like a capital L, it doesn't matter what they plan to do because they won't succeed at any of it. So you better believe I'm gonna grab that collar, stomp that hip, and make them lean forward.

This kind of posture break, where you make your opponent lean forward like a capital L, could be considered an “invariant” of playing the guard. Regardless of what else is going on, going L-shaped is probably a bad move for them.

Invariants that matter

When you're learning a new technique, start by identifying which aspects of the technique are invariants.

It may be a bit of a shocking revelation to learn this, but when you're being taught a new technique step-by-step, most of those steps are optional. They might only make sense in certain situations, or for or against certain body types. In other words, they're variable, which means they're not invariants.

You need to understand which pieces of a technique are variable and which are invariants. If you can't do this, you'll struggle to make any technique work because you won't know which of the steps are situational and which are mandatory.

If something is variable, that means you can use it, customize it, or swap it out to your liking. But if something is an invariant, you need to nail it perfectly every time. Good coaches use invariants as the basis for teaching.

We could spend all day listing invariants in Jiu-Jitsu, but here are a few to get you started:

Get them off-balance before attempting a throw.

Twist their head and spine so they aren't aligned in the same direction.

To complete an armbar, isolate their elbow and bend it over a fulcrum.

To complete a kimura, open their elbow by pulling it away from their body.

To stop them from rotating, control the far limb.

Never let your opponent under your center of gravity.

Pass the guard in three phases: disentangle, control, pass.

Once you start thinking about invariants, you see them everywhere. Knowing the invariants isn't just a hack for learning Jiu-Jitsu techniques; it's a learning strategy you can use to take big first steps when acquiring any skill.

On the podcast:

• Ep. 310: Integrating Theory and Practice, feat. Aldo Vergel de Dios

Further study:

• 80/20 Rule
• Concepts Over Techniques
• Making Smaller Circles