To put it very shortly:
Tetration is a transformation between Euclidean 1D Real Number line and 2-D spinor spaces.
Self root is a transformation between 2D spinor (null-plane, minimal line) space and Euclidean Real number line.
So this is transformation ACCROSS geometries.
Higher hyperoperations and their inverses perfmorm transformations between other geometries ( conformal, for example) and Euclidean.
Non-integer hyperoperations ( whose RANK is non-integer) correspond to transformations from e.g Real number line to a space which has fractional, in between geometry - say geometry in between Eculidean and 2-D spinor space for tetration/selfroot.
It may be called a transitional geometry, transitional state of Geometries, may be transitional non-integer dimension.
Ivars
Tetration is a transformation between Euclidean 1D Real Number line and 2-D spinor spaces.
Self root is a transformation between 2D spinor (null-plane, minimal line) space and Euclidean Real number line.
So this is transformation ACCROSS geometries.
Higher hyperoperations and their inverses perfmorm transformations between other geometries ( conformal, for example) and Euclidean.
Non-integer hyperoperations ( whose RANK is non-integer) correspond to transformations from e.g Real number line to a space which has fractional, in between geometry - say geometry in between Eculidean and 2-D spinor space for tetration/selfroot.
It may be called a transitional geometry, transitional state of Geometries, may be transitional non-integer dimension.
Ivars