When you want to say that someone doesn't know anything about a particular thing, do you say they don't know jack about it, or that they know jack about it?
I've seen it used both ways. Which is correct?
If jack is a quantity of absolutely no value, i. e. zero, then the difference between
He knows zero.
He doesn't know zero.
is basically zero.
Both expressions are "correct" in the descriptive sense that native speakers use both.