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05 September 2013

more on the Space argument

If you have not read TSM, Time Space Material and Infinity, it is one of my most major arguments in favor of Gods existence, and I suggest you read it before this post, which is a continuation of some of the ideas.

A response I once heard to the spatial argument is that 3 dimensional space is in fact wrapped onto a 4th dimensional sphere. Therefore, the size of the universe is fixed. If you travel in one direction long enough you will end up right back where you started. Now, this model contradicts euclidean geometry and has some other problems, but I will leave those aside for the moment. Two things came to mind as a result:

1) You have invented a 4th spatial dimension (the radius of the sphere). Can we travel in it? Regardless of whether we can travel in it, something must travel in it for it to be considered space. This dimension is unlimited and is still subject to the Spatial argument dilemma.

2) In this sphere, several of the dimensions to measure position in space are angles (like theta and phi for spherical coordinates). These dimensions are fundamentally limited to 360 degrees. I wanted to argue that all spatial systems required at least one unlimited dimension, such that whatever spatial system you imagined, the Spatial dilemma still applied. Unfortunately and fortunately, some exist.
Take for instance two points in 3dim space set a fixed distance apart along an imaginary vertical line. Any point in space can be signified by angles from both of these points (relative to the connecting line) and a theta about the center line.
Fortunately, the problem with this is that as points appear farther and farther away, the measurements of the two angles must become more and more precise. For any point distance x away, a precision d can be found to map the point with the angles. Therefore unlimited or infinite precision also produces a spatial dilemma. For if you shrink your viewpoint down to the arbitrary level of precision you reach, the universe becomes arbitrarily large.

2b) This has an implication for the material argument as well, adding weight. As you break down matter/energy into smaller and smaller parts, you are increasing precision arbitrarily. Therefore the dilemma of matter also produces a spatial dilemma even in a spatially finite universe. (Even if the universe is a fixed sphere 1 billion light years in radius, if the breakdown of matter is infinite, a viewer from that size will perceive an infinite universe)

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