Is Inflation Directly Tied to the Money Supply?

How do you define inflation? In some ways it's a slippery thing, like trying to nail Jell-O to a tree. One common definition amounts to "a general and sustained rise in the price of goods and services." Another is "a persistent decline in the purchasing power of money."

Others argue that inflation is directly tied to the money supply. That is to say, they believe a substantial rise in the money supply is the same thing as inflation. (This is one small step removed from Milton Friedman’s old assertion: "Inflation is always and everywhere a monetary phenomenon.")

Why is the debate important? Because of the infamous chart you see below (courtesy of hedge fund QB Partners and the St. Louis Fed) and all the investing implications that stem from it.