Saturday, March 26, 2016

Knowing - Possibility Space



 Given a space, there may be more than one point in space. However for a space with at minimum one point, there may be many values of this point. What is necessary to define a possibility space, is the most basic definition of a point provided, and in addition to that, the prototype of space. The Prototype of Space are the values which the point in space may have. Thus the possibility space for a space with a prototype of "Black" or "White" defines a Binary Possibility space with 2 possible values for one point space. These values may be called images. In general the total frames would be 2^N power for a given space with for this frame There would be 2(N!) total images.

 If one has an infinitely dimensional space, with infinite points for each dimension, the total images would be 2^(INFINITE^INFINITE) frames. If each point where a vector in that infinite dimensional space, with infinite density of points, there would be 2^(INFINITE^INFINITE) -1 frames which would not be quantities expressible given numbers mapped to that original space. Thus these pictures exhaust them.

If any given image contained a value, that we related to another value, some other image could contradict that image, leading to a case where such basic logic could not be true. That is if our decisions depended upon those relationships to hold, possibility space has images then that would contradict that.


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