In gun self-defense, a martial artist should seek that same calmness.
Without commenting on the unarmed self defense aspect of the discussion I will say I have been involved in a few armed confrontations. Two resulted in shots being exchanged by both sides. I can say that, for me at least, everything around me ceased to exist for that brief moment that seemed to be moving in slow motion. My focus was directed solely at the immediate threat. So much so in fact that had there been another, second or third, threat I may have well missed it until too late. The mental reaction was not a matter of training or a conditioned response but rather a matter of an unconsious survival response to the imminent threat.
I was promised a Shortycicle and I want a Shortycicle!