My cousin went to a Quaker high school, so when I went to her graduation, I had the opportunity to attend a Quaker service.
At a Quaker service, everyone is silent until they have something meaningful to say. Then, they say it. Since it was the service before graduation, a fair amount of parents spoke, including one person who kicked off the service by telling a potty training story about his son (I think there was a moral to the story, too...). His son took it well.
There aren't a lot of spaces for silent introspection. We often are in social situations where a few moments of silence creates palpable awkwardness. Even when we're alone, we are often doing something -- watching videos, reading books, sending emails, or even just listening to music. The service I went to provided such a space. It was interesting to be quietly introspective as part of a community of people.
My style is to be introspective in front of a computer so that I can create verbose artifacts, but I can appreciate the Quaker way as well.