Depending on your interests and how much time you spend reading, learning and engaging you may end up being knowledgeable on a whole stack of subjects. When you interact with others without this same intensity your bound to come off arrogant.

For programmers many things are complementary, interests in Maths, Physics, Finance can easily stem from loving the numerical and mathematical aspects of programming. Effective programming also requires good communication skills and tends to require more formal written language to precisely explain more complex or abstract concepts that come with programming, this can lead to other interests to.