Often Misunderstood Concept: 間合い (Ma'ai)
Chinese and Japanese (and I suspect other East Asian?) martial arts traditionally visualised their 間合い as "circles" (actually domes) whereas Western martial arts view them as "boxes" (actually rectangular prisms).
The left and right fighter's territories are coloured in red and blue respectively. The yellow line represents their centre line. Here the red fighter has invaded the blue fighter's Ma'ai - he has occupied the geometric centre.
Commonly understood as merely "distance" in a fight, but that's arguably too simplistic. Ma'ai really looks at each individual's "territories" and how one moves in order to move through, capture and/or defend territory. Chapter 9 of 孫子兵法 (The Art of War) deals with the principle of Ma'ai in what it calls 「行軍篇」(the deployment and movement of troops)
Here we see two fighters launching kicks from their respective Ma'ai. While they are both attacking each other, neither is moving in to either occupy or control the other's Ma'ai. This is a situation of relative stalemate as both parties are equally able to strike at each other; neither party is asserting tactical dominance over the other (this is more of a technical fight than a tactical one).
In my recent sparring with Karateka I've found that I'm often able to gain the upper hand against my partners by simply invading their Ma'ai. I found a lot of the Karateka specialised in ranged attacks - basically launching strikes from their Ma'ai into their enemy's but rarely ever crossing into enemy territory. But once I invaded my opponent's Ma'ai then it often became difficult if not impossible for my them to attack me.
The blue Jujutsu fighter has ducked under a punch and moved in to invade the white fighter's Ma'ai right before executing a take-down. This invasive maneouvre is what allows a Jujutsuka to get their opponent off balance. This is not a stalemate, here the Jujutsuka is forcing a Checkmate.
Ma'ai can be divided into 2 planes -- the "horizontal" boundary between two fighters and the "vertical" centre line. These two planes intersect and form four boxes and as such we see how the basic concept of boxing works.
The Tai Chi fighter on the right has stepped into the Karate fighter's 間合い, represented by the red line that he has crossed over. He is finishing in a solid stance while driving his elbow straight into the Karate fighter's ribs, sending him backwards off balance. Again this tactic is intended to avoid a stalemate and increase the chances of forcing a Checkmate.
Now this is less of a technical thing that a tactical thing. Because by invading your opponent's Ma'ai you are literally starving them of available options that they can use against you. Punches and kicks suddenly become useless at extreme close range and, if I can get close enough, my opponent may have difficult standing upright if I am able to plow through their centre of mass and upend their balance (although I usually didn't go this far as the Karate dojos that I'm training at don't have mats for people to safely fall onto). I'm finding that many people have trained well in learning technical fighting but not so much in tactical fighting. In this sense martial arts suddenly adopts strategic elements and sort of becomes like a game of Chess.
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