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The next diagram geometrically re-visits the physics standard of Heisenberg's Uncertainty Principle. It is treated as an 'indicator', that helps us look for and define new topological functions and relationships. In this case, it becomes a premiere example of how information is transcribed and transduced in to alternative exponential versions of 'dimension'. The Uncertainty Principle is diagrammed as a function which uses the notion that "information" on either side of any and all 'equality signs' stays identical even though the form of the information is codified in what looks like totally different information. They are homeomorphic ... essentially 'identical' ... even though having a different appearance. In the case, it is the 'equality' of Cartesian and Radial information. And, the amended cross-product function is viewed as an operator that essentially transforms two cartesian factors into a singular conic factor.
This is the heart of the Uncertainty Principle. It is a version of dimensional information transduction applied in terms of our specific physical universe. By taking the general process of how information transforms as it gets re-coded in alternative expressions (here being cartesian and conic), and placing into it the real physical constant of the Plancke number, the result is an essential mathematical unit of our universe ... hbar/pi-squared.