One of the other massive advantages of this kind of movement--where one 'falls' into motion rather than 'stepping'--is that it subverts the natural movement pattern that humans expect to see. When people do not have the visual cues of normal movement, they do not 'see' it. If you do not step forward, your head does not bob up or down. If you do not step forward, your feet don't lead a movement finished with your hips. Etc.
These kinds of 'takeoff' movements use a different system of generating forward motion than is typical to the human animal. As a result, if you're clever about it, you can move quite a distance before your opponent sees you. Speed in fighting comes from two places: actual velocity, and the suddenness of movement. Moving without telegraph is 'fast'.
This kind of footwork is fundamental to accelerating without telegraphing your motion.
If it takes your opponent longer to realize what you've done, you can 'teleport' towards them. The result is mentally unbalancing. It can legitimately cause a kind of vertigo. Koryu jujutsu teaches this kind of movement, too. I've had a man execute this kind of movement so quickly and suddenly and without warning, and move into a dominant position, that by the time my mind caught up with things, I literally recoiled like a cat, jumping back. It was too late, and he had already struck me.
There is no hunting like the hunting of man, and those who have hunted armed men long enough and liked it, never care for anything else thereafter.
~Ernest Hemingway
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