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Yes it's very easy to just let things sit at the "acquaintance" level. You know people at the gym, or at work, or at whatever recurring thing that brings you together. But to extend that to friendship, you need to invite them to do something outside of that. Get lunch, come over for dinner, game night, movie, whatever you're into. And then they need to reciprocate at least somewhat evenly. If this doesn't happen it's not really a friendship. And (in my experience) it's very rare for adults to progress beyond the "acquaintance" stage.
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Often i sit around a coffee shop where i work frequently as a remote employee, and I think to myself, "there could be another person here that i have the capacity to be really good friends with but i will probably never know it." And I think about how that's probably true of other people in that coffee shop.

The engineer in me wants to believe some technological solution to finding and connecting with potentially great friends is out there, waiting to be uncovered. But of course, an engineer would say that.

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> there could be another person here that i have the capacity to be really good friends with but i will probably never know it.

I often have the same thoughts. There are many lonely people eager to make friends.

I used to live in NYC where I didn't know anyone. And I remember one evening at the coffee shop in Barnes and Noble, there were only two other people there, and we started to chat. Even though we had very different backgrounds, we started to hang out and became good friends (but lost contact since then unfortunately).

Sometimes it doesn't take much, just exchanging a few words. Forcing oneself to be a bit more social, without expecting anything, is probably a good habit.

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The unstated bit is that you have an incidental excuse to talk to them (compared to cold approaching in other contexts) but you still need to talk to them. Everything depends on you making the effort.
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Compared to a gym, the class setting almost forces you to talk to people. I wouldn't see myself talking to people in a gym, but in a snowboarding club or martial arts class, or a group hike, it's difficult not to. Once you exchanged a few words, even for the sake of an exercise, the ice is already broken. At the very least, you'll say hi the next time you see that person.
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