Even the caterpillars? Can't we talk to the caterpillars?

Theoretically, The gravitational force decreases linearly as you dig down. This means that for every meter down you dig the force of gravity decreases by a set amount. This happens until you reach the centre, at which point there is no net gravitational force (Sort of weightless, so you would float a bit like you were in space). There wouldn't be a sudden switch over as you pass the centre because the force has already decreased so much that it's not noticed. Then as you claw your way back up to Australia the gravitational force will increase linearly. (Now before lots of people jump on my back, the decrease/increase may not be completely linear due to the absence of dirt in the recently dug hole and the varying densities and smoothness of the earth but that gets a bit complicated) 

There is a famous thought experiment about someone jumping into a whole that passes straight through the earth. They accelerate towards the centre and then decelerate until they just reach the opposite surface. Then they accelerate back towards the centre again. Assuming no air resistance they would oscillate for ever.

Back to the digger, the dirt would be a problem to shift. You would need to do work to overcome the gravitational force other wise the dirt would collect at the centre.

Obviously, the earth's core is molten making all this impossible but it would be interesting to try out on the moon.  

I just spooked myself rather badly.

I wondered why Jon and Rob disagreed about the rate at which g goes down as you descend below Earth's surface.

I used about 40% of an envelope to show that, inside a sphere of uniform density, g does decrease linearly to zero as you descend (but I could be wrong). The basic premise is the the matter above your location forms a series of hollow shells, each of which has zero net effect on your weight. Your weight goes down proportional to r-cubed because that's the distribution of matter in a sphere, and it goes up with r-squared as you get closer to the centre of gravity, and the net result is that it decreases linearly with r.

So I assume Jon's non-linearity is a function of density distribution in the various strata, and I am cool with that because I don't have any data, but I would expect crustal rock to be around 2.5 and the iron core to be around 8.0 to 10.0 (under huge pressure), so a considerable effect could be expected.

Then I thought about dark matter and dark energy, and the observed fact that, at galactic scales, the force of gravity seems to suddenly revert from r-squared to r-linear.

http://en.wikipedia.org/wiki/Modified_Newtonian_dynamics

And I thought "Maybe universal gravity isn't true". Newton did intuit that universal law from a rather restricted domain, after all. Maybe intergalactic space is actually 2-D, and it's only the big lumps of matter that make it go 3-D. It could all just be a huge pop-up book!