The problem is your use of the word "new" instead of using the word "different." It's verbal slight-of-hand. Differences are easy to spot but "new" implies some sort of overhaul, a series of changes that goes further than "different." (And, no, I could never pinpoint when one became the other. But I suppose that was your point, wasn't it?)

I am different from moment to moment, but I'm the same for all intents and purposes. I have the same list of likes and dislikes, the same sense of humor, the same speech patters, sexual urges, etc.

TJ today will never be significantly different than TJ yesterday or TJ tomorrow. But, TJ 20 years ago or TJ 20-years-from-now won't bare much of a resemblance to TJ today.

If you replace a new part of your car every once in a while for 20 years until nothing is left of the old car, then it has changed and yet never ceased to be the same car.