I sometimes do. If I get overexcited about something and the other person relates to what I'm saying, I tend to repeat the same few sentences over, altering just a few words, hoping to get my point across even more powerfully than before. Sometimes the other person changes the subject, which tells me that I have said enough about it.
I have a friend who also does this (she is not an Aspie). I love being with her because I can repeat myself and she does as well so we could go on for a long time until we both get bored and change the subject at the same time.
The other day I saw her and she said something like, ''my friend is upset because she forgot my birthday, and I said 'oh don't worry about that, seriously', but she said 'yer but that's not the point, how could I forget a good friend's birthday?' So I said 'yes but I really don't mind,' and she said, 'yes but that's not the point, I didn't mean to forget your birthday and now I feel bad about it', and I said, 'you don't have to worry about it', but she said 'no, that's not the point, I can't believe I forgotten your birthday, after all you done for me', and I said, 'yes but don't worry about it', and she said, 'yes but that's not the point' and I said.......'' She went on like that a few times . But I didn't mind because I could relate to what she was saying so I was agreeing strongly and kind of enjoying what she was repeating. It probably was not how the conversation went with her friend who forgot her birthday, but it was just how she told me.
I think having a friend what shares a social quirk sometimes can be fun for an Aspie.
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