Atlas on Haystacks: inertia and gravitational mass

Pretending to be Atlas holding the world with this erratic boulder on Haystacks reminds me of the problem with two different types of mass. Gravity is pulling down on the boulder so it has weight W=mg. If we tried to push the rock with resultant force F the acceleration would be calculated with F=ma. The equations have the same form. In the second equation, which goes with Newton's Second Law, mass in kg is called INERTIA. It is resistance to change in motion. Now imagine we let the boulder fall, the resultant force would be the weight so we'd get W=ma. Isn't this the same as the gravitational equation? So is g the same as acceleration due to gravity? Here's the problem with the two ways of thinking about mass. For gravitational mass, g is 9.81 N/kg - the gravitational field strength. If we let the mass fall, the acceleration due to gravity will be 9.81 m/s2. Why is this the same size as gravitational field strength? No one quite knows. It is called the equivalence principle. Some experimenters are working to stupid numbers of decimal places to try to measure a difference between the two masses. But maybe they really are the same.