Contradictions in Still and Flow?

I interpret the quote: "Be still like a mountain, flow like a river" as keeping calm and centred even as a whirlwind of activities and other mental distractions, rage around us. Apparently contradictory, it somehow seems to make perfect sense.
I think the sentiment is best understood by example.
It reminds me of scenes in movies like Mission Impossible where super-slow-motion effects show our hero's mental stillness and concentration - come to think of it, Kung-Fu movies have long used this technique. Even as our hero is working double-time to untangle himself from some improbable situation, or fight off impossible odds, these special-effects "show" his brain still working calmly for some resolution. Our hero's concentration slows the external world down and time virtually stands still as he calmly plots his next move, seemingly uneffected by the mayhem around him.
Our hero is in flow ..... performing amazing acts even as his mind is still and focused.
How cool is that!