Infinite Vectors

"All right now, remember. A war is mostly run. We run whether we are defending or attacking. If you can’t run in a war then it’s already over."—Shichiroji, Seven Samurai

Movement, from an idyllic stroll in the park to a sparring match in a ring, can be described by a series of vectors. A vector is a variable quantity that can be resolved into components, it has both magnitude and direction, each movement described by a distance covered in a given time at a specific angle. A rapid advance may be described as a single long vector, while an evasive half turn is described by a series of short vectors of increasing or decreasing angle.

How does understanding a theoretical mathematical construct make you a better fighter? It doesn't. However conceptualizing movement in vectors may help you understand how to vary and texture movement, a valuable skill in setting up offense and optimizing defense. The more uniform your motion, i.e. the more identical your vectors, the more predictable your movement. The greater the variability in vectors, changing magnitude and direction, the more chaotic movement will be and the more difficult it will be to predict your next position.

Let's start with magnitude, the speed of movement, which already allows you two variables to vary. The distance covered and the speed it takes can be varied to set-up both offense and defense. The Starfish would be an example of changing magnitude toward and away from your opponent using essentially the same angle. Another example, would be drawing your opponent on defense, by shortening the distance you withdraw each time to pull them closer for countering.

The other component of the movement vector is direction, that is varying the angle your moving at. Traditionally, martial artist divide the compass of movement into 45° units, which is a convenient if artificial discretization. We have to remember that movement is three dimensional, we're moving both in the horizontal but also vertical planes, thus you are changing angles within the horizontal plane but also above and below that plane. The Corkscrew uses an increasing angle to set-up varied movement. Switching from a left retreat to a right one, is another example of varying angle without changing magnitude.

Thus when we use drills to enhance movement, work on timing, or spar we should incorporate an understanding of movement to enhance our ability to randomize our movement and maximize our offensive and defensive arsenal.