"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 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 in mathematics.

"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 geometrical 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 'PlaneAndSolid' 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

The record (Truly Yours) petitions the Reader to translate the meaning and intent of Buckminster Fuller's above quoted statement. The most comprehensive answers will be published under their author's names (with author's permissions), in the forthcoming 11th edition of TOTAL FIELD THEORY. Hopefully, Readers can see for themselves that this is indeed a very important, correspondingly challenging entreaty. The issued quote is verbatim, by Buckminster Fuller, Copyright 1928. What is Mr. Fuller talking about? What does he mean to convey in this written, published statement about geometry and the 4th dimension?

(( *Truly Yours adds his response to the above statements by Buckminster Fuller. The Reader is graciously invited - if not challenged - to translate the intended meaning of Mr. Fuller's extraordinary statement, as quoted above.
*Perhaps the most prominent fact of palpably angry contention here, is Mr. Fuller's emphasis that, though a geometric point doesn't exist, it is nonetheless: plane and solid geometry shaped spheroidal - round; not cubicle. Emphasizing that when a given Geometric Point (A) moves (A--->B), generating a One Dimensional Straight Line, it does so at right angles - 90o perpendicular - to itself.

Commencing the extrapolation of right-angle-ruled dimensions that follow, from the geometric point to the 2-dimensional geometric Plane (B--->C) and then on to the geometric 3-dimensional Solid (C--->D - empty of - or occupied by - matter or energy) and finally to the (generally unrecognized - popularly - said to be - 'acknowledged', but yet to be formally and academically recognized and functionally applied) 4th dimension of matter (D---E - which is consistently said to be 'invisible', 'immeasurable' and 'unimaginable'): to the electricity moving at right angles from matter (E--->F), thereby defining the 5th dimension as electricity, at right angles (F--->G) to which moves magnetism, thereby defining the 6th dimension. There are no precedents for the herein employed standards of identification and recognition of the 4th, 5th & 6th dimensions.))

But this is only my interpretation. I may have missed altogether, Buckminster Fuller's expressed intentions. What is the translation - the interpretation - of the Reader of this 'New Topic'? (Copyright 1928)

R.S.V.P.
Thank you for reading this missive.

All things bright & Beautiful All creatures great & small
All things warm & wonderful The Lord God made them all