I've always struggled with figuring out what is what function... Si especially.
I can be nostalgic about things that happened earlier in the day!
Also, it's lots of fun to play thousands of songs in my head, and compare the taste of what I'm eating now to what I've had in the past.
I even see the usefulness of tradition now. A continuity of experience that bonds people and society together.
Nostalgia, definitely. Comparing flavors, music; yes.
My family was always big on tradition, and I really liked it as a kid. Evoked a strong emotional response. It's something I want to continue with my son, to a degree.
My husband (INTP) doesn't get the emotional side so much, is a bit like you said, he can appreciate its purpose.
But also, and perhaps even more strongly for me, daydreaming. Not to be confused with crunching thoughts and ideas, but just letting go of it all and fall into a world of wonder and fantasy.
Daydreaming is Si? Is it certain types of daydreaming?
i never really understood cognitive functions that much, but maybe Si manifests for me in my tendency to organize lots of bits of information within collections of things
I just love organising my books/music/movies both physically and online or in computer filing. I can fiddle with that crap for hours on end.
Oh same here, especially about the music library. I've compiled databases for other areas of interest as well. At one time, I had made a database of books I've read but I've since abandoned it.

Sometimes organizing makes me very happy. I've always thought of this as more Te, is it actually Si?
It comes in bursts, suddenly I'll have an impulse to organize something and spend hours madly focused. Probably stop when I realize I have a pounding headache and it's actually 3am. I'm not very good at keeping things organized though...
Also it's in my thirst for knowledge, more particularly, to build up my knowledge base. I want to improve my vocabulary, my skill set, my general knowledge of every subject and memorise basic facts.
I definitely get this... I don't necessarily even have an interest in the specific piece of knowledge, I just want to know everything. It can be irritating. Sometimes I get into these loops of cramming facts into my brain, it can feel out of control and I don't
really enjoy it. Almost feels compulsive. I am much happier when I let my mind relax and flow, exploring thoughts and making connections. Writing is very helpful. Sometimes wikipedia can be the devil.
On the minus side, the Si also has a hit-or-miss quality to it. I can be very attentive to certain details but very ignorant of certain others. If a detail isn't of interest or use to me, it won't likely register. Sometimes this can be embarrasing.
I can never remember people's names. As soon as they say it, it's gone. Do I even hear it in the first place? If I remember to focus and make conscious note when they say their name, I can remember without trouble. But normally I forget to do this... it can get very awkward.
I can never remember where the car is parked. Get lost in ridiculous places. Where things are located in the supermarket, where I set my book. When people call, they seem to expect I will know who they are by the sound of their voice. It's fine as long as I have their number in my phone. Before this, I would always be slightly terrified to answer the phone.
I've gone through entire conversations where I didn't have a clue who I was talking to...
In general though, I have a really good memory. Actually much better than most people I know.
When I was a kid I used to hide this, it made me very self conscious.
Things people said, whole conversations, past events, very specific details. I was always really good at board games and card games as a kid. Would beat the adults. Then people began expecting me to win. It made me hate the games and I refused to play.
I think I know what you mean. I often have to consciously consult myself as to whether I need or want something. Every time someone asks if I want a cup of tea for example, I have to stop and really ponder for a good few seconds whether I do - even then I often end up saying yes or no before I really work it out, because I'm making people wait. I also will sometimes will be oblivious to the fact that I'm feeling tired or too hot or that I have a headache, and then when I realise it, I'm suddenly aware that I've actually been feeling that way for a while.
Sometimes I really dread that moment when going in for a brief visit and someone asks if you want a cup of tea. I normally end up hesitating, and after a moment feel I can't say no, because then they'll start insisting and I'll be too uncertain of my position so I'll probably awkwardly cave. By this time I will realize I actually don't want any tea, but now it's too late. Then they'll want to know what type. And I won't even like the ones they have. So I point to a random one, thinking I'm going to have to drink it because it'd be rude to leave it untouched. All the while my INTP is sending me ESP glares because he's now been cornered into rugby discussion and is being served instant coffee, which he's pretending he doesn't mind.