I also wonder if these personality types are supposed to be immutable, because I suppose it's not dreadfully unlikely that my letter changed because I've shifted my focus from logic, physics, and mathematics to music.
I don't believe any one type of personality can adequately describe one person consistently through their life.
"You are who you choose to be." -- Iron Giant
If the basis of your decisions about who you are choosing to be has nothing to do with the factors that determine personality types, why shouldn't personality types shift? But I have a better explanation (see below)
That's because your sense of self is an illusion. Your brain makes all kinds of arbitrary decisions, and then your consciousness comes along after the fact and goes "Oh, yeah, I did that because of this logical well-thought-out reason." It's actually nonsense, and you're always going to feel like "you" no matter what changes in your head. In fact, if something does change, your brain will helpfully reconstruct your memories of the past to include the new you in them instead of the old you.
Your brain! Adjusting reality to preserve your fragile sense of ego, so you don't have to!
Smuel, that is a load of bull. And what's worse, it is too easy to see as such.
Just because we are capable of self-deception doesn't mean we always deceive ourselves. There are other routes that can maintain one's fragile sense of ego without breaking with Truth.
Kurlan Naiskos from Star Trek (or rather what it represents) -- The artifact that reminded Picard of the philosophy that individuals are communitities and communities are individuals.
We are who we choose to be, and we are sum of all that we were. All the senses of self that we have had, are having, and will have
are part of who we are now. We will deceive ourselves about who we were to our conscience selves if we cannot accept who we were at one moment in time, but that aspect of who we are/were will still impact who we will be. And because we have not experienced our future "selves", we tend not to factor that part of our being into the equation.
Personalities types are an attempt to find order in the chaos that is our soul. The order is the illusion, but the chaos is real.