07/05/2008, 11:26 AM
We can use these twisting or rotation properties of hyperoperations to get a glimpse what in x[z]y y dimensional space is:
We know that ( i may be mistaken in these analogies):
x^x=x[3]x=x[4]2
So according to my conventions, in 2 dimensional space, this is edge x TWISTED 4 times by pi/2, or 2pi, or a TWISTED line, related to torsion of line.
In x dimensional space, it is edge x twisted 3 times via pi/2. So one twist is removed from line and attributed to space itself.
Hopefully this can be extended to lower operations like multiplication and addition and zeration to see their geometrical meaning. Negation as inverse twists and imagination as rotation (?) of edges will follow. Rotations ( imaginations) will lead in case of straight angles to a kind of Hilbert space filling curve with edge x in n or other number of dimensions.
Ivars
We know that ( i may be mistaken in these analogies):
x^x=x[3]x=x[4]2
So according to my conventions, in 2 dimensional space, this is edge x TWISTED 4 times by pi/2, or 2pi, or a TWISTED line, related to torsion of line.
In x dimensional space, it is edge x twisted 3 times via pi/2. So one twist is removed from line and attributed to space itself.
Hopefully this can be extended to lower operations like multiplication and addition and zeration to see their geometrical meaning. Negation as inverse twists and imagination as rotation (?) of edges will follow. Rotations ( imaginations) will lead in case of straight angles to a kind of Hilbert space filling curve with edge x in n or other number of dimensions.
Ivars