If your friend falls in the water or is about to be hit by a bus, getting excited about it doesn't help anybody. You have do something, and quickly, but with purpose and reason.
Surely this is at least somewhat at odds with being calm?!
I had an opportunity to attend a talk where a meditation teacher described his experience dealing with cancer. Prior to being diagnosed he said he had a mindfulness practice outside of formal practice where he would set the intention to be aware of mild discomfort throughout the day and try not to react to it immediately. He provided an example of becoming aware of an itch. Instead of reaching for it and scratching he would try to bring heightened attention to the sensations, discern their qualities (if they were manifesting over a large surface area or small, increasing in intensity or fading, etc.), and try to entertain mind states that had a "if this was going to be my experience for the rest of my life would I be able to make peace with it?" quality. After three breath cycles if the sensation persisted and if he wasn't able to let it just be then he would mindfully scratch an itch. He claimed that working this way, with trivial things like itches or mild joint pain, provided a reservoir of equanimity that he was able to draw from when experiencing chemotherapy and the rest.