Is the mere fact that I know someone but derive no value from them a reason to continue a friendship?
Hi Sergius, welcome to the forum.
As you state it in this quote, I’m sure you know the answer is, “No.” You wouldn’t continue a friendship, because you wouldn’t be friends, if you honestly derived no value.
But, is there really no value in seeing him every once in a while… no friendship at all? As was implied in your post, there are many degrees of friendship and acquaintance… relationships of all kinds, really, even romantic ones, mentor-type relationships, etc. And relationships aren’t stagnant, either. They evolve forever as people learn and change through the course of their lives. This particular friend has something that not many others do: a longer perspective on your own evolution as a person, and shared experiences from prior stages in your life. That can be fun to remember and talk about, or to get his reaction to something recent you’ve decided to do, him knowing you a little deeper than others. How fun it is or how valuable his reaction is to you depends on him, the person you’re remembering with. He may be too different to really be in contact with at all anymore. As with all relationships, you judge as you go and use how you feel about the person as a general barometer for continued interaction. I once had an old high school friend “de-friend” me on Facebook when we had not exchanges messages of any kind, my guess is because of our polar political views. Oh well, and I really don’t hold it against her. We are much too different now. On the other hand, I am still good friends with someone from high school who is a True Believer of God. We simply avoid the subject and focus on the ways we get along.
Sometimes, it can actually be painful to be around someone, clinging to the memory of how well you used to get along, as compared to how different you are now. But, only you can be the judge as to how much and in what way you want to continue a relationship. A lot of times, it just happens naturally. If one person, or both, don’t really want to hang out any more, they just stop putting forth effort to do so.
Edit:
Here is an old thread I started a while ago similar to your question, where I received some valuable responses: The Value of Relationships