Myth of 4-D 'supercube'

[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

[mkirkpatrick]

I am sure you could work something out here Rascal,make it fit so to speak,btw,in the UK
we have an oxo cube for making gravy,though I suppose that's not anywhere near being
"super"!




regards michael.

[RascalPuff]

I am sure you could work something out here Rascal,make it fit so to speak,btw,in the UK
we have an oxo cube for making gravy,though I suppose that's not anywhere near being
"super"!




regards michael.

________________________________

Mr. Fuller's poiint here seems to be that the popular icon of a 'supercube'is fallacious, regarding illustrations and/or sculptures representing the 4th dimension.

Although a geometric point doesn't exist, its (mathematical) shape is not to be thought of as being square, but, rather, round. As sequential perpendicularities emerge with projections of right angle motions, a sphere, and not a cube, is produced, in a three dimensional construance.

Ripples from a center source of disturbance are round (not square).

A free falling drop of water spontaneously takes on a spheroidal shape.

Soap bubbles, for example, naturally take on a spheroidal shape. The physical dynamics of a soap bubble are extremely complex with regard to surface tensions and other balanced factors of tensor integrity.

Among other conclusions, we may draw from this the fact that the morphological quality of the 4th dimension is applicable to and observed - in situ - in quite any shape at all; beginning with a microcosmic spheroid.

(All of this seems to be Fuller's way of noting that the dominant paradigm of a 'supercube', is a really square idea, as it is popularized to exhibit the 4th dimension.)

Best regards,
- RP

[mkirkpatrick]

I tend to agree Rascal,that natural symmetry is spheroidal,it seems to be the universal
signature of form and force as expressed via energies motions.

The cube,square,and the triangle,are all expressions of the circle or sphere,I think we
get confused with too many forms?basically there is only circle! The one form.






regards michael.

[Profpat]

I'M ALL FOR CIRCLES AND SPHERES BUT COULDN'T YOU HAVE A HYPERSPHERE A SPHERE WITHIN A SPHERE?

I THINK TO CAPTURE THAT 4TH DIMENSION OF TIME YOU WOULD NEED IT. THE SPHERE ITSELF IS STATIC NOT MOVING OR DYNAMIC. TO GIVE IT MOVEMENT THROUGH PAST ,PRESENT, AND FUTURE YOU REQUIRE SPACE.

IN OTHER WORDS I BELIEVE I HAVE MY OWN PERSONAL HYPERSPACE. iT STARTED WHEN I WAS BORN AND IS WITH ME NOW. iTS MY OWN PERSONAL SPACE THAT I CREATED THROUGHOUT MY LIFE.

JUST A THOUGHT.

PAT

[RascalPuff]

I'M ALL FOR CIRCLES AND SPHERES BUT COULDN'T YOU HAVE A HYPERSPHERE A SPHERE WITHIN A SPHERE?

I THINK TO CAPTURE THAT 4TH DIMENSION OF TIME YOU WOULD NEED IT. THE SPHERE ITSELF IS STATIC NOT MOVING OR DYNAMIC. TO GIVE IT MOVEMENT THROUGH PAST ,PRESENT, AND FUTURE YOU REQUIRE SPACE.

IN OTHER WORDS I BELIEVE I HAVE MY OWN PERSONAL HYPERSPACE. iT STARTED WHEN I WAS BORN AND IS WITH ME NOW. iTS MY OWN PERSONAL SPACE THAT I CREATED THROUGHOUT MY LIFE.

JUST A THOUGHT.

PAT

__________________________

Indeed, prof, the 4-D sphere is a hierarchy of spheres within spheres, ad infinitum.

Good thought.

Best regards,
- RP