[RascalPuff]

"In reality, mathematics can say very little about the 4th dimension. There is nothing in the hypothesis of the 4th dimension that would make it inadmissable from a mathematical point of view, this hypothesis (*sic) does not contradict any of the accepted axioms and, because of this, does not meet with particular opposition on the part of mathematics.

Mathematicians even admit the possibility of establishing the relationship that should exist between 3-D and 4-D space, i.e., certain properties of the 4th Dimension. But they do all this in a very general and indefinite form. No exact definition of the 4th Dimension exists (*sic) in mathematics (*as opposed to the fact that an exact definition does exist in geometry, and, whereby mathematics is by routine academic-scientific standards, authoritatively based).

"The basis of the denial of the fourth dimension, which has been supported by the theoretical and fallacious plane and cubical geometry, has been the inability to produce an additional or fourth perpendicular to a cube, as the basis of an additional power multiplication, whereas, poor little plane arithmetic and algebra, without geomentrical reference, being abstract, indicate the perfect ability to do so.
"Very rightly do they do so, for if the geometrist will go back to his first perpendicular, he will find it perpendicular to a sphere, for did he not assume a dot as his first basis of a geometrical theorem, which if conceded at all, must be spheroidal.

Matter, if existent at all (and we cannot fallaciously assume a truth that is not), must be spheroidal. Surely the 'Plane And Solid' geometrist does not claim his 'dot' or 'point' to be cubical, for then he would have no further cause for his progressive antics.

We see that there is no cubism, and that we can have as many perpendiculars to the inside or outside of the sphere as we may wish.

Each power raising, or root taking, is on the basis of spheroidal increase or decrease by that many units of its radial or time dimension. The only 'straight line' then is the radial or time line, demonstrated by spheroidal dissection on its radial axis. There is also much laughter at the 'Plane&Solids'.
- R Buckminster Fuller, 4-D TIMELOCK, p. 17

Regards,
-RP