The use of possessive pronouns in phrases like "I don't know my geography" or "He certainly knows his Star Wars"

Solution 1:

Although I can't give a "formalized" explanation, I wanted to look at using the possessive with personal nouns in the same way that you've done in your examples. Imagine the following situations and example utterances:

Situation 1: Your wife, Sarah, is suspected of giving aid to known terrorist organizations.

I know my Sarah. She would never be involved with something like that.

Situation 2: Your son, John, was offered a college scholarship an account of his high marks in high school.

That's my Johnny. He's always been such a bright pupil.

In this usage, the possessive is used for providing emphasis -- the object is something that the possessor is intimately familiar with. Notice that you can make the same statements without the possessive:

"I know Sarah. She would never be involved with something like that."

The statement is the same but the fact that "Sarah" is an object which the possesor is intimately familiar with is minimized. The semantic difference is small, but I feel it might be similar to emphasizing certain words in particular sentences. (e.g. compare "Are you wearing that dress to the banquet?" to "Are you wearing that dress to the banquet?")

She knows her Star Wars.

She knows her world history.

She knows her calculus.

For these formulations, I'm tempted to interpret the possessive exactly as above (used for emphasis), but one can't ignore the particular phrase "to know one's X" as idiomatic. When you say "she knows her X" this tends to identify X as an area of specialization. For example

Fred knows Python.

(= Fred knows someone called Python => We might guess Python is a person in this case)

Fred knows his Python.

(= Fred is well versed in Python => We might guess Python is an area of expertise, e.g. the Python programming language in this case)