Monday, March 22, 2010

Theory of the Fifth Dimension - PART I: Summary of "What is Where, up to now"

This came to me one day when I was having lunch at the Bishop Mountain Hall cafeteria. In enjoying my meal, I lost track of time and did not realize the time that had passed. These thoughts gave rise to the theory of the Fifth Dimension.

DEFINITION

I'll begin with a definition of "dimension": property of space (dictionary.com). Mathematically, there exists a 4-Dimensional world. While modern physics theories have suggested up to 12 dimensions, I'm not getting into that. Five is enough for me.

KNOWN DIMENSIONS

We start with 1D, it's simply a virtual point. Take a point on a Cartesian plane for instance, the point (4,3) is not the same as (3.999999, 3.000001). One could extend this argument that a point is finite, therefore infinitely small change to it entirely changes the property of the point. The "Big Bang" theory gave rise to the concept of compacting infinity into a point in space. Therefore a point is infinitely small or infinitely large, depending on its parameters.

2D is simply a plane, 3D is the dimension of the world we live in; we can mathematically represent any physical object. As an analogy, 3D maps "what is where"; for example, a treasure box with width of 20cm, length 40cm, and height of 50cm, is located at the location (400, 300, -20).

Einstein's Special Theory of Relativity brings 4th Dimension into consideration. The 4th Dimension is somewhat non-trivial, it consists the property of time. One can think of the 4th dimension as the independent variable that corresponds to a 3D representation at that instant. Take the previous example, the 4D addition would be, "The treasure box....on January 8th, 1991.

Now... the fifth.

PROBLEMS WITH THE 4-D

Though the 4D is sufficient to map "What is where at what time, up to now", it did not take in the account of the human mind. I shall introduce the 5th Dimension in PART II

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