Let me preface this post by saying that I enjoy nothing more than spending time with my son: playing with him, teaching him, sharing in his wonder of each new discovery. I still carry him often throughout the day, and will continue to do so for as long as he will allow it (unless my back starts rebelling again...). Equally entertaining is watching the interaction between my son and my nephew. At their age they more play AT each other, rather than WITH each other.
That said, I also understand the need for my son to learn how to spend time and play by himself. I cannot possibly spend every waking moment of my life entertaining my son, and to try and do so would inevitably fail.
I also understand the value of children learning to work things out for themselves, rather than expect others (a parent, professor, etc) to referee their lives. I know that I'm the sort of mom who could easily become a helicopter parent, and I don't want that for my son.
I play with my son, as well as with him and my nephew. We sing songs, dance, go to the park, talk, and play in the sprinklers. But for much of the day, I encourage them to interact with each other as much as one should expect of two young toddlers (usually about 10 minutes at a time, but sometimes as much as half an hour when they get interested in something). When they steal toys from each other, I don't jump in to interfere. I've yet to get the feeling that one is intentionally picking on the other, so unless someone is hurt or about to get hurt, I try not to interfere - at least not right away. We are working to teach Aidan that though life doesn't always go the way he wants it to, there are things he can do to make it better. If he can't work something out, the appropriate response is to leave and go elsewhere, rather than to harm or scream, and then to tell me what happened later so we can discuss it.
So obviously these lessons are works in progress, but it's what we focus on day in and day out. I have so many hopes and dreams for my son, but the most important of all is that he grows to be a caring, confident, and intelligent individual.