This may sound stupid, but this is something I can't seem to wrap my head around.

If you were to stand in the dead center of the south pole, why wouldn't everything be up-side-down? Why is it that you are standing at the very bottom of the Earth, everything would still appear the right side up?

There is no preferred up/down direction in space. The only thing that gives gives humans a perspective on what is down is the direction of gravity. So whatever direction gravity is pointing is the same direction you perceive as down. At the south pole, gravity points directly upward(from the perspective of someone on the north pole) but in reality, gravity just points to the center of the earth, so that is the perceived direction of down. Obviously, someone at the south pole could be just as justified as you are in wondering why someone on the north pole doesn't see everything upside down.

To give another perspective on the matter, think of you standing wherever you live with a table standing next to you, with it looking right side up, just as it should. It looks the way it should because the legs of the table are pointing downward, but as explained above, this just means the legs are pointing in the direction gravity is pointing. Now you and the table are instantly transported to the south pole. With you standing at the south pole your legs are pointing in the direction of gravity, just as they were before, and also the table's legs are pointing in the direction of gravity, as before. So everything is just as it was.

The only difference is that you and the table were both mutually rotated through some common angle. However, the laws of physics are invariant to rotations through an angle, so everything should look the same, as it does.

^what he said

to expand upon this say the core of the earth was hollow, and asuming the density of the earth was all completely eual if you were in the centre of the earth would you be weightless?

Actually, if you were anywhere inside of a hollow sphere, such as the Earth(assuming the Earth is perfectly spherical and hollow) then you would be weightless. You do not need to be in the center, you can be anywhere as long as your are inside of the sphere. This follows from a theorem in mechanics known as the shell theorem. Basically, it is true, because if you are closer to one area of the sphere, the stronger gravitational field from that area, since you are closer, is canceled by the larger mass of the rest of the sphere. However, keep in mind that was a simplified explanation, and you need to use calculus to prove it.

by your logic, that must mean to be completely upright, you have to be standing onthe north pole. i assume youre not living on the north pole, but if what youre saying is true, you must be slightly slanted, which you are not
http://www.themapcentre.com/acatalog/UpsideDown.jpg

this picture is perfectly legitimate

Actually, if you were anywhere inside of a hollow sphere, such as the Earth(assuming the Earth is perfectly spherical and hollow) then you would be weightless. You do not need to be in the center, you can be anywhere as long as your are inside of the sphere. This follows from a theorem in mechanics known as the shell theorem. Basically, it is true, because if you are closer to one area of the sphere, the stronger gravitational field from that area, since you are closer, is canceled by the larger mass of the rest of the sphere. However, keep in mind that was a simplified explanation, and you need to use calculus to prove it.



Same goes for electric field inside a hollow conductor, no?
And for all inverse-square vector fields, right? (assuming that the force is the inv. sq of the distance, and the shell is homogeneous in terms of mass/charge/whatever)