The Built-in Assumptions of Algebraic Geometry

 Just as Cartesian space limited by being fixed to an incomplete numerical structure with the complex rotational action of the imaginary number i missing, the matrix algebra of Grassman, while mechanically useful, carries with it certain wrongheaded assumptions about infinity. 

The solution was developed by Gauss, yet not put into direct use due to his uneasy political position of being the standard bearer for contemporary mathematics with its strict shibboleths. This Riemann was able to draw from Gauss the necessity of other geometries wherein the Euclidean flatness of space was violated. And significantly the possibility of the projective infinite "point" to be well defined in a curved phase space. Revolutionary, and not in keeping with the bad infinity night in which "all cows are black" of endless non transformational sameness of space itself. 

And for all that Riemann developed as distinct geometric possibilities of metastasis of transformation, yet only partially adapted to physically causal space, the full essence of this quality of revolutionary ideas was  up till now only adequately captured in art. This is due to a humanist polemic delivered unmediated as the sense of vision or hearing otherwise as unspoken fugal drama. Yet not a drama that may be criticized in the same way as being a referent to the limitations of historical finiteness of perspective. Its beautiful essence simply is. Nothing more nothing less.

When this higher species of transformational noetic mentation is demonstrated to be put into use, it necessitates conformity with its higher lawfulness. Thus as humanity emerges as an outer space residing civilization the lesser limitations of assumptions about human beings must be re-examined and false belief systems shed and adoption of a new visionary program for continuing development of scientific power made the essential framework for one’s worldview. If we are to not merely survive but strive toward a more perfect and prosperous unity, then those that matter will be heeded.