Saturday, 19 December 2009

Three Dimensions: Where did they come from?

Though it makes me far from the objective of these blogs, as one reader has contacted me regarding the previous comment and has asked me this question I add this short comment here. How man understood that he is living in a three dimension space? It is from builders experience since the ancient time. To build a wall straight we use a piece of heavy plumb and string. To make a floor straight what do we need? A flat floor means for us that water do not flow on any direction on it. It is enough to check only two directions on the floor among infinite directions. It is easier to take those two direction perpendicular, in right angle, to each other. Builders do it by fixing two straightened perpendicular string drawn on two sides of a floor. With these three string we can build a room with straight walls and flat floor. We never need more than that and these tree strings in a corner create a 3-dimensional Cartesian coordinates system for the room, for the space that we live in. Further if you make each of these floor strings in right angle to the string of plumb, then the water will not flow in any direction on the floor. Floor will be "leveled," as it is said. If the floor is small compared with the radius of earth it is consistent with water flow. This floor made by perpendicular to the line of the plumb is actually a surface tangent to the sphere of the earth at the point where the tip of the plumb touches the earth and if it becomes larger in lengths then the water will flow to the tip of the plumb from all directions. It is equivalent of a pendulum, indeed. In imagination, one can use it in ocean for converting very tall water waves, to re-wind up the damping pendulum every now and then, to electrical energy. Locally, it is said, surface of the earth is a collection of these small flat surfaces. Intrinsic geometry of the earth surface can be studied with these two dimensions. This floor also is called to be a chart at the touching point of the plumb. Earth surface is a collection or an atlas of these local charts many of them folded together in the atlas. Hence the earth surface is a manifold.
(c) Copyrighted materials, Copy rights, Peter Jones December 2009.

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