I like to think of normalcy as having everything going as expected. Of “knowing” the correct response to a situation that life throws at you, because it has been successfully dealt with before many times.
If an old rural Chinese person comes over to the US, they might find what we find normal (sit down toilets, our relative “lack of face/honor," children not being expected to take care of their parents/grandparents, etc) at odds with what they think of as normal. Just as we would find his way of thinking and acting as strange.
The (what is the opposite of normal in this sense? Strange/novel?) respective strangeness we mutually feel towards each other’s customs is a short-circuiting, or a blindness, of our ways of thinking/acting before this novel experience presented itself.
I feel that to live a normal life, is to live by a “complete enough” rulebook that your society/ecology has taught you and your ancestors over the years. This way of life, if followed, will lead to your success within the community; as everyone you know plays by the same rulebook and gives them all, more or less, the same preconceived notions. But once met with the different value system of another society, all sorts of misunderstandings will happen.
The more normal a person seems, means that that person conforms more closely to society’s standards. But it also means that that person cannot innovate, as innovation requires breaking society’s preconceived notions.
Take the Persians, for example: everyone in the known world at the time had red and blue dyes; but the Persians had a natural source of Purple. Wars were fought over this new royal color. But all of that death could have been avoided if only people realized that if they mixed red and blue dyes together, they could make their own Purple.
Or take writing, or art, or comedy, or anything else. All of those things, in order to touch your soul or spark your mind with an Aha! moment, either gave you a new way of seeing/experiencing something (otherwise if it was the same, it would be common and boring) or it gave you a new idea that was wrapped up in just enough familiarity to keep it both relatable and enticingly alien.
Like how no one painted in perspective until the renaissance; or how comedians present us with something normal, and then twist it enough for us to see it in a light that highlights its absurdity.