*u̯id-

The core idea of this root was:

seeing

This is still visible in the branch around the word vision  but the family has also taken on the sense of knowing and the tree of words is quite impressive.
Here’s a little (incomplete) overview over the words that are more vision based:

• vision, video, visible
• evident
• view
• interview
• review
• visit (“going to see”)
• envy (originally “look at, upon”)
• provide, provision (“foresight”)
• improvise 
• supervise (“look over”)
• voyeur (“looker”)
• envisage
• visa (“paper that has been seen”)
• deja vu (“already seen”)
• Gwendolyn  (“white, shining, easy to see”)
• Penguin (“white, visible head”)

And here’s an overview over offspring that are more about knowledge:

• wit
• wise
• wisdom
• Druid (“tree-wit”)
• guide
• advice (“knowledge, perspective toward”)
• history (originally: “knowledge, insight”)
• story
• idea (“what you see/know”)