Here’s a source for that quote I failed miserably to paraphrase:
“So what is this mind of ours: what are these atoms with consciousness? Last week’s potatoes! They now can remember what was going on in my mind a year ago — a mind which has long ago been replaced. To note that the thing I call my individuality is only a pattern or dance, that is what it means when one discovers how long it takes for the atoms of my brain to be replaced by other atoms. The atoms come into my brain, dance a dance, and then go out — there are always new atoms, but always doing the same dance, remembering what the dance was yesterday.”
–Richard Feynman (The Value of Science)
Also from that site (not really a cite, since it’s just the first blog I found with the quote):
The brain changes connections, some old some new. To use a cimbersome example:
I played trumpet from the time I was a child until well after college. To this day, I can pick up a trumpet and sight read and play music. I don’t think about it, it goes from the score to the instrument. I may have to practice difficult parts but the notes nor the timing is never what are the problem.
As an adult, I taught myself to play the flute. But I can’t sight read like I can with the trumpet. When I attempt to play scored music, my brain says “C” (Ok, fingers do a “C”) “Bb” (OK fingers, do a Bb).
OTOH, I was never able to improvise on the trumpet, but I can wail on the flute. I can “instinctively” detect the key and even key changes and play counter melodies on the fly.
Different pathways, different results.
Your brain constantly adjusts itself and develops pathways that mean you aren’t even the same person from minute to minute.
Have you even had a sea change of your world view based on a reading or a speech? You aren’t the same.
I will tell you what does not change (for the most part): your value system. Your sense of right and wrong is what you hold onto for a sense of self. Not the funky gray areas (“is it OK to kill someone that will kill someone else?”) but the basic underlying values. Those are ingrained and are, more than anything else, what make you YOU.
It’s funny how a brain, that seems so material, can generate such an enigmatic result. Don’t get hung up on the materialistic aspect of the brain. Whatever we are, we are a pattern that emerges from it. Like music from a violin, our brain is the instrument, but “we” are the song. For some damn reason, that “song” is aware.
I believe the answer to the OP’s question is both yes, and no, depending on how you look at it. I would like to believe the ‘yes’ trumps the ‘no’, but who can be sure? And does it really matter?
Would we react the same way to the same stimulus from day to day? Probably, but maybe not.
We aren’t robots and our experiences inform but don’t deny us their value. And this is without including in our reasoning the Elephant in the Room, Mr Id, as exemplified by Peter Griffin.
No, we aren’t the same person moment to moment. We are a chain of identities linked together from birth to death, connected only by physical continuity and an illusion of “personal identity”. This is the definitive answer.
A neurologist on NOVA ScienceNow a day or two ago said that every new memory leaves a physical change in the brain. So, he said, “If you learned something today, you don’t have the same brain you had this morning.”
If that’s true, then only those who refuse to learn are the same persons, moment to moment. That’s why I feel more like I do now than…Hey! Wait a minute. Who did I say I was, again?