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I don’t think I have intrusive thoughts. I’m happy, generally pretty creative (hobbies, coding, etc.). Sometimes politics and world affairs get me down, but I don’t feel like they are “intrusive”, more like affecting my mood. I like how /u/[email protected] put it–I kind of let my mind do whatever it does, and I try to be an observer of what unfolds. I think meditation practice has helped with this practice (Vipassana or Insight meditation specifically).
It’s just a guess, but zen & yoga are often related in Western culture because of the way Buddhism and Hinduism were introduced together in the West.