The distinction between Empty and Emptiness is all that is necessary to construct traditional mathematics. The empty simple space is the foundation upon which a deeper understanding of the process of creating symbols can be built. In its essence, the conversion from emptiness to empty space is the process of picking up a piece of paper with the intent to Record Tokens. It is an acknowledgement of a sentience that is creating symbols. As a starting point, the genesis of an Empty Space from emptiness incorporates the mathematician as the fundamental mathematical construct. Next, I (William Bricken) will attempt to demonstrate that this distinction is indeed informative.
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BRICKEN, William, 1986. A Simple Space. Advanced Decision Systems. 1986. pdf 
[Accessed 15 December 2023].